His words appeared to contradict coach Louis van Gaal, who had earlier said that he was "99 percent" sure that an attacking player would join the Bavarian giants, potentially even in the coming week.
"I think that he was talking about Arjen Robben, who is coming back after his injuries," said Rummenigge, according to the website of German daily Bild.
"Seriously: we will sign no new player in January."
Bayern recently signed the Brazilian midfielder Luis Gustavo for 15 million euros from Hoffenheim.
The 23-year-old is expected to join up with his new team-mates at the start of the week at a training camp in Qatar.
He could replace Dutch veteran Mark van Bommel, the Bayern captain, whose contract expires in June and who has been linked with a move to Wolfsburg.
Before flying to Qatar on Sunday, Van Bommel, 33, said: "Anything is possible -- that I leave during the winter transfer window, that I stay until the end of the season, or even that I extend (my contract)."
He added: "The transfer window has only just opened... Nothing is definitive yet, loads of things could happen.
"Lots of people are interested, which makes me proud. I've already turned some of them down."