Neuer will enter into the final year of his current deal at the end of this season and talks have already begun to extend the deal further.
An agreement is yet to be reached between the two parties but Neuer recently expressed anger that wrong details of ongoing contract negotiations with the club were being leaked to the public, with some reports in Germany suggesting that the 34-year-old is demanding a new five-year contract worth €20m per year.
"We both know what we have in each other," Rummenigge 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."
Since moving to Bayern Munich from Schalke nine years ago, Neuer has won seven Bundesliga titles, four DFB-Pokals, one UEFA Champions League among numerous honours while also tasting glory at international level by helping Germany to World Cup glory in 2014.
Bayern Munich have already struck a five-year deal with Schalke 04 goalkeeper Alexander Nubel to arrive on a free transfer at the end of the season.