Yes, you can reference this character providing you respect registered trademarks, and follow the conditions of copyright and patent laws. After researching the LEGO Millennium Falcon I realize it is quite a fascinating toy. Your character would have spent many happy hours putting it together and playing with it. I can see it becoming a central symbol in your story. You can certainly use the name of the toy if you properly capitalize the words. More on this below.
To help readers like me who are unfamiliar with Star Wars understand the toy and associated games he played, you can describe his memories of assembling the thousands of bricks and parts of characters and machines. You can describe the thrills he experienced as he made one character do this (e.g. fly the plane to [name of place]) or watched another character do that (e.g. shoot down the plane with [name of weapon]). Doing so will not violate copyright even if those things happened in the real story.
To get an idea on what you can do with copyrighted material, see Wikipedia's description of the story of the novel Millennium Falcon written by James Luceno. Referencing toys or books or other items by their patented names/titles in one's story is completely acceptable so long as one capitalizes the appropriate letters. Not capitalizing the proper letters is a violation.
In the case of this toy, the first word LEGO is all capital letters. The name of the toy is LEGO Millennium Falcon. The LEGO Millennium Falcons all have big numbers attached because each model was different. However, unless your character has two models that he compares, you won't want to include five-digit numbers in your story. If you want, you can do like Wikipedia does and just call it Millennium Falcon.
I'm not sure why Wikipedia omits the word LEGO. However, LEGO makes many other toys besides the Millennium Falcon. From Wikipedia/Lego:
Lego (...stylised as LEGO) is a line of plastic construction toys that
are manufactured by The Lego Group, a privately held company based in
I include that quote partly to show the word "Lego" both with all caps and with only the first letter capitalized. I find this rather confusing with regards to the copyrighted name of the toy. However, all the listings for the toy that I saw in my Google Search used the LEGO form of the word.