There are three issues here: copyright, trademark, and plagiarism.
Copyright law explicitly says that you can't claim a copyright to a phrase or slogan. If what you have in mind is some clever turn of phrase or witty line, there's no legal barrier to using it.
Quoting classic phrase is generally not considerred plagiarism, as long as you don't imply that the idea is original to you. Lots of writers include phrases from Shakespeare, the Bible, and other well-known sources, old and new. If it's an old book, this is often considered educated and sophisticated. If it's a new book (or song or movie or whatever), it's considered trendy.
Like, people often say things like, "After my company lost that big contract, I could see the handwriting on the wall", without mentioning that "the handwriting on the wall" comes from the Bible. Or referring to a couple facing challenges as "star-crossed lovers" without citing Shakespeare. Etc. It's perfectly fair and legitimate.
I'd avoid using a borrowed phrase in a way that implies that you made it up. Anyone who has seen the original will think less of you. But just using it in the proper context is fine. If I'm quoting a phrase or sentence in a way that could be taken to imply I made it up, I'll often toss in a disclaimer like, "Like they say ..." or "As the old saying goes ..." or "I once read ...". Or if I want to be slightly more formal, give a casual citation, like, "Winston Churchill once said ...".
Also note that plagirism is not a crime, but an academic violation. You can't be sued or fined for plagiarism. If you plagiarize in an academic environment, you may lose your job or be publicly humiliated, but you won't go to jail. Plagiarism does not really apply to fiction.
Trademark: A company will pretty much always have a trademark to their brand name and may have a trademark to an advertising slogan. That doesn't stop you from using the word or phrase, but it limits how you can use it. Like the CocaCola company pretty regularly sues people for using "coke" as a generic word for any brand of cola. Sometimes it comes down to the capitalization: If you say in your book, "Fred ordered a sandwich and a Coke at the restaurant", CocaCola will smile happily at the free advertising. But say "... and a coke ..." and if they see it, they'll sue you, because now you're using their trademarked name as a generic word. Briefly, if you use a trademarked name to refer to the company owning the trademark or to the appropriate product, there should be no problem. The problem is if you try to use somebody else's trademark to refer to something other than their product.
