This role (if the movie even happens of course) should be very hard to cast. Harrison Ford managed to make Han Solo a brash, arrogant, cocky, fearless, charming (I could go on forever with the adjectives) character, while also coming across really cool, and - crucially - not in the slightest bit annoying. We've seen many attempts at the "Han Solo type" in the years since, and witnessed how difficult that is to pull off. So who on Earth could step into those shoes and play Han Solo Jr.?
Well, there are two ways they could go: Look for an actor that resembles Ford, or don't think too much about that and focus on someone who can best convey the essence of the character. Now obviously in a perfect world we'd get both, but I won't hold my breath. The problem here is that - unlike say Michael Fassbender portraying a younger Ian McKellen - Ford played Solo when he was still relatively young anyway, so they will probably feel added pressure to lean towards matching up physical appearance - in my opinion this is a mistake. Sure the guy should be handsome, and not look a million miles away from Ford if it can be helped, but we all know what wonders a bit of Hollywood magic can work on an actor's appearance anyway. Bottom line is this role will require a GREAT actor with charisma and screen presence to burn first and foremost, and he rest can be worked on.
So with all that in mind, here are your choices. I also included the usual suspects - the LaBeoufs, the Hedlunds and the Francos etc. There is an "other" option too of course, so if you think I've looked someone over click that and let me know in the usual spot.