Golovin has a lot of potential. Technically and workrate-wise he's got everything needed to develop into an excellent CM, also already has a good vision\decision-making feel about his playing. Possibly a bit lightweight for some tactical setups in a better league, and would maybe need to focus on developing certain things rather than trying to be such an all-action player, it's hard to say if he's physically up to carrying that sort of veratility up the leagues.
Overall though i'd say he has an argument for being among the best 2-3 Eastern European CM prospects since Modric, who was on a similar level to Golovin right now when i started following him in his last season at Zagreb, with similar questions in my mind as to how he would step up.
However, though it's much better than staying in the RPL, i wouldn't favour him going to a team quite as big as Manchester United. Russian football has fallen into a really bad way this past decade, which is the first where the post-soviet football systems(or lack of them) have had to entirely stand on their own two feet and been found entirely lacking. With such a slim production line of players this generation and players staying at home being the norm, the pressure and expectation on him from the Russian sports media would be considerable. I'd prefer him to go somewhere where less is expected to get used to a new culture and tougher league, as Russian\ukrainian players seem to have a harder time adapting in general, even without much pressure than players from most other European countries.
tbf, a lot of that struggle was down to the unique challenges facing the late 80s\early 90s players being the first to move abroad and having to tackle the massive changes in coming from a communist setup. Those issues aren't there anymore, so maybe i'm just too cautious but with such a small tradition of moving abroad(only really one and a half generations of players) and seeing recent players like Yarmolenko, Zhirkov(though there were bad knee injuries at play there too) and others have a tough time, i'd err on the side of caution with any player that is still a prospect. I'd want him to get much more playing time than Zinchenko has at Manchester City