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Alaba is expected to re-enter negotiations with the Bavarian giants once their European campaign is over and Rummenigge believes an agreement will be reached.
"With Alaba, I am cautiously optimistic we will find a solution," Rummenigge told the media on Tuesday.
His comments may come as a blow to Pep Guardiola, with the Manchester City manager having been linked with a move for his former defender in recent months.
City are looking to rebuild their defence after their disappointing domestic season and Alaba's experience and versatility would be prized assets in the Premier League.
Bayern aren't expecting such a busy window after already completing their marquee summer signing.
Having already signed Leroy Sane from City in a deal that could reach €60m (£55m/$67m), Rummenigge insisted there will be no further significant outlays.
Bayern opted against exercising their option to make Philippe Coutinho's loan from Barca permanent and any lingering hopes of remaining in Munichappear tohave been dashed.
"Coutinho - as I said, the contract is running out and we cannot and will not make any further investments of this magnitude," said Rummenigge.
Bayern have also ruled out a potential big-money move for Kai Havertz , whose long-running transfer saga could now be closer to reaching a conclusion.
Leverkusen had been adamant that Havertz would not be sold before their Europa League campaign was over, but they were knocked out at the quarter-final stage by Inter on Monday .