The Portuguese midfielder sealed a £67m move to United in January, leaving Sporting Lisbon to put pen to paper on a four-and-a-half-year deal at Old Trafford.
And he was thrown straight in at the deep end by Solskjaer, making his United bow in their 0-0 draw at home to Wolves last week.
Fernandes now has to wait until February 17 to make his second appearance for the club, with a trip to Chelsea in store after the Premier League’s winter break.
United are filling the gap in their schedule by heading to Spain for a mid-season training camp, which will give their new midfield recruit a decent chance to fully integrate himself into the squad.
Nevertheless, Solskjaer is already impressed with Fernandes’ attitude, insisting his discontent with last week’s debut is “a good sign”.
“I’ve kept in touch with him. He’s had a few days back home to organise,” he told United’s website.
“He’s going to have to move house and say his goodbyes back home, so he’s ready.
“He wasn’t 100 per cent happy with his debut and there’s more to come, so that’s a good sign.”
United find themselves six points adrift of the top four with 13 games left to play in the 2019/20 campaign.
Solskjaer, though, is hoping the newly-devised winter break will help galvanise his side ahead of the business end of the season.
“It’s important that English football got this break,” he said. “Whenever it’s going to be I think it will benefit the players and benefit the teams.
“December and January were really hectic with loads of games, nine in each of those months, so our players were stretched and yeah, it’s a good time for us now.”
He then added: “We go to Spain and it’s a chance now to regroup and evaluate what has been good, because we haven’t had time to do too much training, so we’ll get a good seven, eight or nine days of training before Chelsea and the rest of the season.
“Hopefully we’ll have two games every week, so that’s the biggest part, reintegrating and restarting again, because there have been loads of positives, a few negatives, and we’ve just got to make sure that the end of the season is going to be a good one.”
Another man joining United on their trip to Spain is Scott McTominay, who has been out injured since their 4-1 win over Newcastle on Boxing Day.
“Scotty has done better in his recovery than we thought, so we will take him with us,” Solskjaer said.
“Hopefully he can join in the training sessions and Axel [Tuanzebe] as well, he’ll join in, so that’s two positives and it’s a good chance for them to use this time with the players.”