Boateng, 29, reportedly turned down a potential move to Manchester United in the Premier League but remains a strong contender for French champions Paris Saint-Germain, according to Le Parisien paper. Negotiations between the player's management and PSG are taking place behind the scenes, reports Xinhua news agency.
Following Bayern's narrow 1-0 pre-season friendly victory over United at the Allianz Arena, Boateng admitted to Mourinho that he would not move to Old Trafford. However, several star names of the Bayern team are demanding that Boateng stays.
At club level, Boateng has struggled for more regular game time across the past three seasons, due to both discipline issues and injury, and Bayern are thought to be happy to let him leave for the right deal and price.
United are understood to have had a £22.5million offer rejected though the club maintain they only wanted a loan. Former Dutch worldwide Arjen Robben has warned the club's leaders not to underestimate Boateng's value to the team.
Bayern face Eintracht Frankfurt away in the Super Cup on Sunday before the German Cup begins next weekend and they start the Bundesliga at home to Hoffenheim on August 24.
Bayern however would be able to sell the centre-back to a continental club, such as PSG, until the end of the month.
"We've had success with him a lot in the past and I know him very well".
Robben, who has played alongside Boateng in six title-winning Bayern teams, indicated that he would be disappointed to see the World Cup victor leave the club. "He is one of the world's best, and we need his physical presence on the pitch".