The 19-year-old academy graduate has enjoyed a remarkable ascent since making his debut in March 2019 and was shortlisted for the PFA Young Player of the Year award after a stunning breakthrough season.
Greenwood scored 17 goals in all competitions last term and went on to make his senior England debut in September, only to be sent home by Gareth Southgate after breaching their strict bio-secure bubble in Iceland.
There has been more talk about the teenager's behaviour in the last week and Solskjaer denied on Monday that the forward was subject to any disciplinary action, having missed the trips to Newcastle and Paris St Germain.
Reports have since emerged suggesting that Greenwood has been warned about his behaviour, but the United boss dismissed that and any talk of his time-keeping being an issue.
"You do (make a target for yourself) when you play well and I'm not concerned at all with Mason making a target of himself," Solskjaer said.
"He's come in, he's played fantastic, he played his first league game against Tottenham last season, was brilliant and just kicked on.
"Yeah, he's made a mistake this summer with England and suddenly the whole English press go after him and that's something we've got to look after.
Anthony Martial, Jesse Lingard and Eric Bailly are among the unavailable players on Saturday, when United continue what has been a strange season for them and everyone else.
Tuesday's impressive 2-1 triumph in France means they have won all five of their away matches to date, yet they have lost both of their games at an empty Old Trafford.
As if the shock 3-1 loss to Crystal Palace was not bad enough, Solskjaer's men went on to be smashed 6-1 by Tottenham and desperately need a change in fortunes when Chelsea visit this weekend.
"The league this season has started strangely," said Solskjaer, whose side welcome RB Leipzig in the Champions League on Wednesday and host Arsenal next weekend.
"It is a very, very strange atmosphere within the stadiums. It's not the same. It's not like it used to be. Without the fans, it's more sterile.
"After the win against PSG, you feel it's almost like you've been to the training ground and done well in training. The edge is missing.
"For me now, we need consistency. We've been too much up and down. We need to address the home form.
"The next week is a great test for us because we all remember what happened after the last time we beat PSG. The response wasn't the greatest was it?
"This week is a chance for our players – and also staff – to show that we've moved on from that time."