Structurally dialogue goes in quotes and you don't vary from that unless it's very beneficial, intuitive, and your audience will accept it.
What POV is your novel written in? A conversation in 1st, 2nd, or 3rd with their various "flavors" (cinematic/omniscient/close) will look very different when one of your characters is at a distance.
What is the point of the conversation? Are you: looking to drop information, trying to develop characterization, ramping up conflict, offering a panacea, or something else? The point of the conversation and it's greater position within the book will tell you how much information is needed.
What is the pace of the book at the time that you are having the conversation and what is this conversation going to do to that?
Why POV matters
1st person is going to hear the conversation, but it's going to give the reader subcontext. So you likely will have that inner monlogue (italics) going on if its engendering a lot of thought. And it's possible that the narrator will "space out" and miss part of the conversation. In which case the reader only hears the bits of the conversation that the narrator pays attention to. In this form you likely do want all 2nd party communication in quotes.
2nd person is going to be aware of what went on as they were told it happened. In which case they might only hear the person on the phone on the end that is observed. This gives you the opportunity to hide what's going on, but to see the outward effect on the person who had the call. You also have further ability to narrate, pause, and introduce subtext.
3rd person is going to have the most variation since 3rd person could know everything or just be hugging close to your protagonist. The omniscient 3rd or even the cinematic could essentially perform that "split screen" view you sometimes get in a show where you can see both kids in both bedrooms talking and doing their various things. But, you can also keep the dialogue on the otherside of the phone hidden by having the narrator more interested in describing something else. If you're close 3rd, this could be the same function we saw in 1st, an examination of how the conversation affects the speaker. Or, maybe the narrator, is more focused on the killer that's hiding in the closet or outside the window; so the phone conversation is only given the barest treatment.
Conversation Purpose & Pacing
If your conversation is trying to provide information, you likely are using the phone conversation as an info dump. This can and should be done when info needs to be supplied quickly, but its also a trap as, done to often, it becomes a bore. Usually these types of scenes need to be short to avoid the pitfall and are better if the information is provided in a new way (excepting the case where your characters are way too interesting and can make phone conversations between themselves interesting).
If you are trying to ramp up tension, then its possible the information imparted does that job, but its also possible that withholding something will give the reader a tense little puzzle to solve that imparts more to the story than you can by telling.
A phone conversation is a good way to slow the pace of your novel, so it might be good as a sequel following action to release, but not alleviate tension (research: scene-sequel for more info).
If you're trying to change the relationship of characters then the characters will push eachothers buttons in good or bad ways and the focus will be how those button presses change the conversation and the dynamic between those characters.
All of this is to say: Writing a phone scene on a novel should do the barest minimum to accomplish what it's trying to do and the way you do it (abbreviated/protracted; direct/meandering; personal/detached; detailed/obfuscated) will tell the reader a log. There's no right way for the generic phone conversation, but you can turn these "knobs" on any conversation to create the conversation your story needs.
For further information you may just want to look into how to write good dialogue. At the end of the day that's what a phone conversation is and you write it, largely, as you would write any other piece of dialogue or plot element: There should be a conflict. You should determine if it's resolved or not. And then you should make something worse in someway by the end of it.
Ok, so how does this inform the written structure or "markup"?
Given @cloudchaser's post on the use of italics, you'll note that neither thought processes nor dialogue should use italics by convention. However, two sections imply you may still have cause: You can italicize these words from the phone if you wish as it would fall under "far away" depending on your circumstances or "from a device". However, in both cases you still use quotes.
If you have decided to display the text as heard from the 2nd party, then your structure can correctly italicize or not italicize the text. And the reasons you would do italicize, if you even choose to render the text for the reader (we're assuming the dialogue exchange is important enough to do on screen at this point), are going to be the affect on the reader's understanding. Distance or emphasizing the device both will mechanically change the feel of your story, if your target audience is capable of understanding the convention. You may need to provide context clues to impart the meaning: disrupted voice from electronic degradation, a distance from the phone that affects the understanding of the dialogue, or some other point that falls under those two elements. Most of these considerations fall under purpose/pacing. How much time will you have to give context clues? Do You want to? Will emphasizing either of these things distract from the main event or add to it?
If you've chosen an omnicient POV, it is likely that you can't justify distance as a reason to use italics. If you are showing both characters with omnicient or 3rd person-cinematic pov, you likely can't justify distance or mechanics. If you are using 2nd person pov, it is likely that the use of italics will confuse the already nested nature of the story if that narrator isn't in some way focused on the device.
Ultimately, the use of quotes/italics will be a stylistic choice; which your editor may have more to say on given the style-guide for your publisher. The trend tends to be to not italicize any of it and to use quotes even if you do. @cloudchaser's post is formally correct, but not indicative of use by popular authors. If best means "sellable" as it often does to me; it's more about the elements I've described than grammar-level rules.