The Basques are adamant that they will not accept an offer below €40 million for the versatile Spain international, who can play in midfield or defence
The Basques are refusing to allow the Spain international to leave San Mames unless somebody activates the player's buy-out clause of €40 million.
And Rummenigge freely admits that the Bavarians are not in a position to meet such an asking price and claims that their rivals for Martinez's signature, Barcelona, have no intention of doing so either.
"I'm not optimistic, to be honest," he told TZ when asked about the deal. "[Athletic's] president [Josu Urrutia] has always emphasised that he doesn't want to sell the player for a price under the clause.
"That's an amount of money that hasn't existed in Germany before. There is no club in Europe that is willing to pay that price. I have a good relationship with Barcelona, and Barcelona aren't prepared to do so.
"You have to see the whole transfer business very rationally. There are some players who are worth it, but not many in this world."
Consequently, Rummenigge is remaining coy on whether Bayern will dip back into the transfer market this summer, explaining that decision lies with sporting director Matthias Sammer and coach Jupp Heynckes.
"I spoke with [Sammer] on Friday," the former West Germany international explained. "Matthias is making an analysis of the current situation, and then we will all agree: if there is a need for improvement, we will deal with it.
"It is often the last two or three per cent which decides whether you become German champions, win the Champions League, or whether you unfortunately don't.
"And Matthias has a very good relationship with Jupp Heynckes. Jupp is very happy that he has Matthias at his side.
"If the need is there, and there are interesting people on the market, we will do something. I can now predict, however, nothing serious. But the board is giving the green light [for further activity]."
Bayern finished second to Borussia Dortmund in the Bundesliga last season, were routed 5-2 by the same opposition in the DFB-Pokal final, before losing out to Chelsea in the Champions League decider on penalties.