Two senior stars who have been in impressive form over recent weeks were left out of the Red Devils’ starting XI for a Premier League trip to Craven Cottage on Saturday.
England international forward Rashford was able to take a place among the substitutes, but Swedish centre-half Lindelof missed out completely.
Solskjaer told MUTV of those selection calls: "There are a couple of niggles, Rashford got a dead leg against Leicester. We don’t want to risk him.
"At the back, Victor is out, not really a concern, he should be okay for Tuesday."
United will face PSG in midweek as they take in the first leg of an eagerly-anticipated Champions League last-16 encounter.
The Ligue 1 leaders will be paying a visit to Old Trafford for that contest.
Solskjaer will hope to be at full strength for a crucial clash, especially as PSG are set to be without the mercurial talents of Brazilian striker Neymar through injury.
Rashford could be the man to make a difference on the grandest of stages, with the 21-year-old having starred as a central striker since United took the decision to part with Jose Mourinho.
He has registered six goals since Solskjaer took the reins in December, with his performances keeping £75 million man Romelu Lukaku on the sidelines.
The Belgian will get an opportunity to impress against Fulham, though, as he steps in to fill the role of lone frontman – with Anthony Martial and Juan Mata providing attacking support from wide.
In all, Solskjaer has made six changes to his starting line-up from the one which edged out Leicester 1-0 in United’s last Premier League outing.
Lukaku, Martial and Mata are three of those to come back in, with Diogo Dalot, Chris Smalling and Phil Jones – fresh from committing to a new long-term contract – also recalled.
Rashford is joined by Jesse Lingard and Alexis Sanchez on the bench.
United will be looking to make it 10 wins from 11 games under Solskjaer when they tackle Fulham, with an interim manager yet to come unstuck across all competitions.