Fernandes was instrumental in the 3-2 win over Atalanta on Wednesday, creating two goals in the second half as United battled back from 2-0 down. The Portugal international was not able to train on Friday and is one of "two or three" carrying knocks ahead of Liverpool's visit to Old Trafford.
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"It was a great comeback which will bring some knocks and bruises which you will expect," Solskjaer told a news conference on Friday. "It's Friday, the game is on Sunday so we'll give everyone time.
"We might have the whole squad back fit or we might be two or three players down. We didn't have everyone [at training] today but let's see on Sunday.
"We have two or three carrying knocks from the game. I hope I can pick from a fully fit squad or I might be without two or three. Bruno might be a doubt but he's doing everything he can to be ready."
Solskjaer eased some of the speculation surrounding his future with victory over Atalanta, a timely boost after the 4-2 defeat to Leicester City. It was United's third win in their last eight games and the Norwegian is hopeful the second-half performance against the Italians will trigger a return to form.
"Hopefully it's the end of a bad period for us," he said. "Good teams come together and if that was the start of something, that's what we hope and the focus and determination of the lads have been really good since Leicester."
United lost 4-2 to Liverpool at Old Trafford last season and have won just one home game against their rivals in the league since 2015. Beating Jurgen Klopp's side on Sunday would leave United just a point behind in the table but victory for Liverpool would open up a seven-point gap after just nine games.
"Every time you play for Man United you play for three points," Solskjaer said. "To be seven behind is going to be a big distance but so early in the season, every game matters just as much.
"We saw last season every team goes through a bad spell. We are chasing them.
"Liverpool are one of the teams we are trying to catch up on, even though last season we were ahead of them, maybe because of bad luck with injuries. We know we still have to improve to get up to the level of their last four years."