The 34-year-old's deal expires at the end of 2020-21 and there has been no breakthrough in talks over fresh terms.
There were reports Neuer was demanding a five-year deal worth €20million annually, but he rubbished those suggestions in an interview with Bild am Sonntag.
Neuer also made it clear he is unhappy with the way certain details around the discussions were being leaked to the media.
Rummenigge, though, is confident both parties will find a way to keep the Germany goalkeeper at the Allianz Arena.
"We both know what we have in each other," he told Bild on Monday. "And under these circumstances, I am optimistic that we will find a solution in the end and that Manuel Neuer will sign a new contract.
"We have the world's best goalkeeper and we have already won everything with him."
When asked about Neuer's anger at the leaks of his contract talks, Rummenigge replied: "His interview was only yesterday, so we could not react to it yet."
Neuer's future has been further complicated by the fact Bayern will sign Alexander Nubel from Schalke on a free transfer on July 1.
The 23-year-old's arrival has also cast doubt on the prospects of Sven Ulreich staying at the club, but Neuer's present understudy plans to fight for his place.
His agent, Jurgen Schwab, told Kicker: "Bayern are a meritocracy, where sporting decisions are made.
"Let's see who ends up behind Manuel Neuer on the bench."