Bayern Munich chief executive Karl-Heinz Rummenigge is "cautiously optimistic" that David Alaba will sign a contract extension with the Bundesliga champions.
Versatile defender Alaba has less than a year remaining on his existing deal at the Allianz Arena but, according to reports, the club are unwilling to meet his demand for a €20 million (£18m/$24m) annual salary.
Hansi Flick has expressed his hope that the Austria international will finish his career at Bayern, who are gearing up for a Champions League quarter-final against Barcelona in Lisbon on Friday.
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 Munich appear to have 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 .
Chelsea are strong favourites to sign Havertz this summer but Leverkusen chief Rudi Voller has made it clear that if a buying club doesn't pay their full asking price, they won't be signing him .