Having come close to signing Boateng while in charge of Manchester United, Mourinho intends to try again for the Germany international this summer.
Off contract in June, Bayern have announced the 32 year-old will not be offered new terms and instead will be allowed to leave at the end of the season.
Mourinho is keen, but will face competition from Barcelona, where new president Joan Laporta is working extensively in the Bosman market given the delicate financial situation he has inherited.
Bayern chief Hasan Salihamidzic declared this week: "It was a joint decision of the club's management and coach was also involved. I explained that to Jerome, he understood it and he will leave by the front door."