"We all know that a sports manager is also needed at Bayern," said Rummenigge after Uli Hoeness was re-elected as Bayern's president on Friday at the club's annual general meeting.
"We will have one in the not-too-distant future.
"We have someone at the back of our minds, but he still has to play football at the moment."
Lahm, who captained Germany to the 2014 World Cup title in Brazil, has a Bayern contract until June 2018.
The defender, who joined Bayern as an 11-year-old in 1995, hinted this month that he may retire from all football at the end of this season.
The 33-year-old has also said in interviews that he can imagine moving into management with Bayern.
The club has been without a director of sport since Matthias Sammer stood down this year on health grounds after suffering from a "minute circulatory disorder in the brain", according to the club.
Meanwhile, Rummenigge says he has "complete confidence" in coach Carlo Ancelotti.
Last weekend, Bayern were knocked off the top of the Bundesliga table for the first time since September 2014 having lost 1-0 at Borussia Dortmund.
They host Bayer Leverkusen on Saturday night and are winless in their last three games, for the second time since season under Ancelotti, following Wednesday's 3-2 defeat at Rostov.
Their Champions League defeat means Bayern will finish second in their group behind Atletico Madrid.
Having won the Bundesliga title at a canter for the last four consecutive seasons, Bayern are in the unusual situation of being second in the table behind new leaders RB Leipzig, who beat Freiburg 4-1 on Friday.