The England international has been one of the Premier League’s standout performers this season, while Villa have been in excellent form with 26 points from 14 games so far.
Grealish scored a brilliant goal in Villa’s 2-2 draw with United at Old Trafford last season.
And Solskjaer believes United will face an even better prospect on New Year’s Day.
‘He is player for Aston Villa and England and has only improved,’ said Solskjaer.
‘I don’t want to say too much about other teams’ players but, of course, he’s a player we know we need to look out for.
‘He scored a brilliant goal last season and we’ve face him enough times last season to know it is going to be a difficult game.’
Solskjaer also hailed Villa’s start to the campaign, while Dean Smith’s side head to Old Trafford unbeaten in their last five Premier League games.
‘They’ve been brilliant, I have to say,’ said Solskjaer.
‘Dean Smith’s done a fantastic job we played them in pre-season they beat us then the one game we had before the league.
‘When you beat Liverpool 7-2 you know there’s not just defending, there’s counter-attack, there’s quality players and that was the game maybe everyone will remember from this season.’