The Bavarian club are understood to be tracking Ajax's 18-year-old defender Matthijs de Ligt, highly-rated by a number of top clubs, should Boateng move elsewhere this summer.
The 29-year-old German international will not be short of possible routes out of Germany this summer, with a number of major European clubs said to be interested in the player.
According to SportBild Boateng may be looking at a move to either Real Madrid or Barcelona, who he has turned down in the past.
Manchester United have tried to sign Boateng previously, but an injury deal prevented that deal from going through last year.
Mourinho's team are understood to likely come after the experienced German defender again, as well as city rivals and Boateng's former club Manchester City.
Paris Saint-Germain are also said to be potentially interested in the defender, though with the Parisian club skating close to financial fair play regulations already they are unlikely to be the German's next destination.
Bayern will be happy to let the rumours and speculation surrounding Boateng to develop whilst the German features at the World Cup this summer, hoping that interest from a number of top clubs sparks a bidding war and pushes up the price.
Boateng played 31 times in all competitions for Bayern last season, as the Bavarians won the Bundesliga title in remarkable fashion - finishing a comfortable 21 points clear of second-placed Schalke.