The France international, whose deal expires in 2010, has been unsettled this season and recently criticised coach Ottmar Hitzfeld for playing him out of position.
"Willy had a chat with (incoming coach) Jurgen (Klinsmann) and he wants to use this chance to stay with Bayern," Rummenigge told the city's Tz newspaper.
"However, it will be absolutely necessary that Willy works really hard on himself next year and Jurgen has made that clear to him."
Sagnol asked for a transfer in December when he failed to make an immediate return to the first team after a lengthy injury absence.
After finally getting some games under his belt, he withdrew the request only to see another injury set him back again in February.
His return last month was equally slow, but the 31-year-old is back in the Bayern first team and appears to be settled again in Bavaria, despite reported interest from Italian clubs Juventus and AC Milan.