Sanches is expected to leave Bayern on loan, having started just six league games in his first season at the Allianz Arena after a €35million (A$51 million) move from Benfica.
But Bayern are keen to hold on to the midfielder due to his potential after he impressed in Bayern 3-2 victory against Chelsea in Singapore on Tuesday.
AC Milan and Manchester United are among the clubs to have been linked with a move for the Portugal international, with Rummenigge claiming a long list of clubs have enquired about Sanches.
"There are at least 10 teams after Sanches," Rummenigge said to Gazzetta dello Sport.
"Conte asked for some information about him after Tuesday's match because he knows he can make the difference on the pitch.
"[Bayern head coach Carlo] Ancelotti was pleased with his performance against Chelsea so we can make a decision on him later."
Sanches told Bild earlier in the week that Milan represented an "interesting option" as he would receive more playing time than at Bayern.