Manchester City confirmed this week that the club’s record goalscorer Aguero will leave the Etihad at the end of the season once his contract runs out after a decade of trophy-laden service.
It has been suggested Aguero would like to stay in England with Chelsea and United among the clubs who have been tipped to make a surprise free transfer swoop for the Argentine, 32.
United may have a need for a new frontman with Edinson Cavani out of contract in the summer and the Uruguayan yet to sign an extension to stay at Old Trafford.
But Borussia Dortmund’s Haaland, who the Bundesliga side want at least £127million (€150m) for if the Norwegian is to depart the Westfalenstadion this summer, is the top target for the Red Devils.
Barcelona and Real Madrid both held meetings with Haaland’s representatives, his father Alf-Inge and agent Mino Raiola, this week as the pursuit of the 20-year-old hots up.
Yet Solskjaer insists United, as they did with Bruno Fernandes, are happy to wait to land their top targets despite the competition from not just Spain’s top two clubs but also Chelsea and Man City.
There is long-term interest in Haaland from United and they were keen on the towering centre-forward when he played for Molde and also when he played for Red Bull Salzburg, before he opted to join Dortmund in January 2020.
Yet even if they miss out, Solskjaer has ruled out moving for veteran Aguero, insisting it does not sit right with him that players can swap between rival clubs, as Peter Schmeichel and Carlos Tevez have famously both done.
“We’d all like the squad sorted as soon as possible but I’m not the one in the trenches with the negotiations but so far we’ve done a really good job,” Solskjaer said.
“We had to wait for Bruno Fernandes but we knew he was the one and that worked out well.
“This summer there’s an opportunity even though this window will be different to any other because of the pandemic and the money teams have lost.”
On the possibility of signing Aguero, he added: “When I played for Man United, if a rival club tried to sign me, and I had gone… well where’s the loyalty?
The 23-year-old has nine goals and nine assists in 29 Premier League matches this term and has been playing through fitness problems, having pulled out of the England squad over the international break.
Rashford’s agency have gone as far to say it’s been two years since the United academy graduate played while fully fit.
But Solskjaer said: “I don’t have any concerns about Marcus’ general fitness at all. Every footballer carries a bit here and there. Very seldom do you say you’re 100 per cent fit.
“I’ve been impressed by his resilience and robustness. He wants to play. He’s got a character that even if he feels something, he doesn’t want to miss games because he loves Man United and football too much to dip out.
“He wants to give everything. That’s all credit to him but, of course, the little knocks he’s carrying we have got great staff to look after him. But it’s not been too big a concern or worry.
“There has never been a risk that we felt will damage him. It is just the way it is when you’re a professional footballer with a game every three or four days.
“It’s been relentless this season so we’ve not had the time. Sometimes you can send them away for a week to a sunny place and that will hopefully come back again so that we can look after the players.”