United tried unsuccessfully to bring the Frenchman to Old Trafford for a loan in January.
But the Red Devils remain attached to the World Cup winner, who is struggling to settle in the Allianz Arena.
Tolisso joined Bayern from Lyon in a record Bundesliga transfer of £ 37 million in 2017, but suffered a serious knee injury the season after winning the 2018 World Cup.
He has played a small role in the current campaign, but the German giants were unwilling to weaken their midfielder depth by letting him go in January.
Despite this, the Sunday Express reports that United remains keen to bring Tolisso to Old Trafford, this time as part of a permanent deal this summer.
The Red Devils are aware that Paul Pogba has not yet accepted a new deal and is linked to a move to Real Madrid and the former Juventus club.
As such, they selected Tolisso as a potential replacement for his French teammate.
United hopes they can rejuvenate the 25-year-old’s career so that he can reproduce his best form.
In the 2017/18 season, Tolisso won the Bundesliga and scored 10 goals and provided seven assists in 40 appearances in all competitions.
However, United will need to be convinced of its suitability before formalizing their interest, as Tolisso underwent surgery to repair the ankle ligaments last month.
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The report adds that Bayern will not block Tolisso’s transition to the Premier League as they seek to fund a deal for 24-year-old Manchester City star Leroy Sane.
The German winger is a long-term target for Bayern and they aim to get it at a bargain price.
Sane’s contract at the Etihad stadium expires next summer and he could even leave for as little as £ 40 million.
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