Manchester United boss Solskjaer will look to sign as many as five new players when the transfer window reopens at the end of the campaign.
The Red Devils will also look to get rid of some players, however, following a season of mass turbulence over at Old Trafford.
Manchester United could lose Ander Herrera to Paris Saint-Germain on a free transfer, while Paul Pogba is attracting interest from Real Madrid.
Matteo Darmian, Marcos Rojo, Alexis Sanchez and Eric Bailly are also facing uncertain futures at Old Trafford.
And as is Romelu Lukaku, whose agent recently hinted at a summer exit amid links to Serie A trio Inter Milan, AC Milan and Juventus.
Solskjaer, though, has promised a cutthroat approach as he aims to turn United into title challengers next season.
“I’m under no illusions that this is not going to be plain sailing,” said Solskjaer. “It’s going to be hard.
“It’s going to be survival of the fittest or survival of the best. That’s how ruthless we have to be.
“We need players here who are going to be able to take us forward.
“That means the culture in the dressing room and what we do every single day here to make us challenge again.”
Solskjaer admitted that United stars are now playing for their futures, while lauding Fred and Scott McTominay.
The duo impressed as the Red Devils slipped to a narrow 1-0 Champions League defeat to Barcelona.
And Solskjaer was enthused by the application of the United duo, saying: “I think they’ve done that since I came in, really.
“We have a certain standard here. We had a great boost [at the start], but now it’s more challenging times with the results and performances.
“You want to see players step up now and say: ‘I want to be part of this’. You saw Fred and Scott McTominay the other day take up the mantle.
“That’s what we expect from all the players. When you win 5-0 or when you’re 3-0 up, or when you win five games on the bounce, it’s easy.
“It’s easy to be a footballer. But it’s not always easy. You get through tougher times. You’ll lose games and your character is revealed.”