Manchester United are hoping to add Varane to their ranks, with the Real Madrid star eager to come to the Premier League.
But, while that’s currently the case, Solskjaer is also looking to reinforce his midfield.
In recent days, United have emerged as potential suitors for Saul – who Atletico want to sell in order to balance the books in the wake of the coronavirus crisis.
Liverpool have been linked, while Barcelona held talks with their La Liga rivals about a swap deal that would see Antoine Griezmann return to the Wanda Metropolitano.
Yet the Daily Mail say optimism is building over at Old Trafford, with the Red Devils convinced they can sign the player for £45m this summer.
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It’s claimed that Liverpool, at the current moment in time, are unlikely to buy unless they sell another midfielder.
And it’s also said that talks with Barcelona have collapsed, with wages becoming an issue for Ronald Koeman’s team.
United are reportedly ‘best placed’ to sign Saul, which is being treated separately to their pursuit of the midfielder’s team-mate Kieran Trippier.
They’ve discussed landing Rennes midfielder Eduardo Camavinga, who is widely considered one of the most-talented midfielders of his generation.
However, they’re more inclined to wait another year given his contractual situation – with the 18-year-old having just 12 months left on his current deal.
Bayern Munich’s Leon Goretzka has also been earmarked as a potential recruit.
But his preference would be to stay at the Allianz Arena, which is why United are looking at other areas of their squad instead.
Now, United appear set to go after Saul.
And whether they’re successful in bringing the 26-year-old to the club, years after Louis van Gaal rejected the player, remains to be seen.
Last year, former Red Devils star Paul Ince urged his old team to bring Saul to Old Trafford.
“What United fans want is exciting players and heroes in their team,” he told the Daily Star.
“There hasn’t been enough of those in recent years at United.
“You look at Manchester City. They’ve got Sergio Aguero, Kevin De Bruyne and David Silva – at least three legends.
“It’s the same now with Liverpool. United don’t have that at the moment.
“I’ve watched Niguez for the last two or three years and I really like him.
“He’s got a lovely build and can score some special goals.
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“There’s a culture about him and he’s still young with plenty of potential.
“The thing is, he won’t be cheap – that’s for sure.
“And, if you look to get him in, you have to think about what happens to Paul Pogba.
“There’s also talk about Felix, but he struggled in Spain – and there’s still a ferocity to the Premier League.
“You’ve got to think about if they can come in and play straight away.”