The 29-year-old is set to leave Bayern Munich this summer having failed to agree on a new contract which expires next year.
Liverpool are interested in signing the Spain international and the midfielder has reportedly held talks with Jurgen Klopp to discuss a move to Anfield.
However, the Premier League champions have not yet submitted an offer to Bayern Munich, who are demanding a €30m (£27m) transfer fee for the player.
According to Dagbladet in Norway, Solskjaer has now spoken to Thiago to discuss a potential switch to Old Trafford this summer.
But Solskjaer is not prepared to sign Thiago on his current wage demands and United will not press ahead with a deal unless the midfielder reduces his expectations.
Speaking this week, Bayern Munich head coach Hansi Flick admitted that he still expects Thiago to move clubs this summer.
‘I assume he will leave,’ he told Bild.
‘We were completely focused on the Champions League, and his contract wasn’t an issue in the past few weeks.
‘We haven’t had another conversation now, but I think his decision has been made.’
United also remain hopeful of signing Jadon Sancho from Borussia Dortmund, while Solskjaer is also looking to add a new central defender to his squad.