Manchester United manager Solskjaer has been linked with moves for Coutinho and Koulibaly this month.
The Red Devils have endured a difficult Premier League season so far, despite recent wins over Cardiff, Huddersfield, Bournemouth and Newcastle.
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Jose Mourinho was understood to be compiling a list of Manchester United transfer targets prior to his departure.
But, now that Solskjaer’s in charge, fans have pondered what that could mean.
Philippe Coutinho has emerged as a target following his struggles over in La Liga with Barcelona.
Koulibaly, though, is Red Devils chief Ed Woodward’s No 1 United target.
Yet speaking after Saturday’s 2-0 FA Cup victory over Reading, Solskjaer admitted he did not expect any reinforcements.
“I don’t expect anyone to come in,” he said.
“Obviously if the club have targeted and identified a few and I think they might fit here then I’ll give my thumbs up.
“But it’s not just my decision. I’m happy with the squad I’ve got.”
Many United supporters have been begging the club to invest in a new defender.
But former Red Devils hitman Dimitar Berbatov feels the rejuvenation of Phil Jones and Victor Lindelof means that is not necessarily required.
“I have said in this column before that United need a new ball-playing centre-back,” he said.
“But the likes of Lindelof and Jones are now showing that they are more than capable of bringing the ball out so they don’t need anyone else.
“Ole instead needs to focus on bringing the best out of the players already on the books and there have been some good signs there already, with Marcus Rashford looking very sharp and even Alexis Sanchez joining the party at Newcastle with an excellent assist.”
United are next in action against Tottenham next Sunday (4.30pm).
The Red Devils lost 3-0 to Mauricio Pochettino’s side earlier this season.