The Spaniard spent last campaign on loan with Italian side Napoli and it was believed that the Liverpool keeper would sign for them on a permanent deal.
However Reina is now set to join Bayern for £2.5m after he agreed terms with the Bundesliga champions and Rummenigge insists that the World Cup winner was keen to push the deal through.
He told the club’s official website: “The player is scheduled to come to Munich for a medical in the next few days and sign his contract.
“Pepe Reina really wanted to join Bayern Munich. He was prepared to undertake this adventure, although he knows he has Manuel Neuer ahead of him, a first-choice keeper who will, provided nothing untoward happens, remain number one.
“Our goal was to be prepared for every eventuality in this particular position. We’ve now settled the situation regarding goalkeepers.
“We’ll go into next season with these three.”
By Phil Wellbrook