Ancelotti was abruptly dismissed on Thursday in the wake of Bayern’s 3-0 Champions League loss at Paris Saint-Germain the previous night.
Hoeness told German radio station FFH: “We’re not under any pressure, but after the two weeks (international) break we want to have a solution.”
Assistant coach Willy Sagnol, the ex-France international, will be in charge of the team for Sunday’s Bundesliga outing at Hertha Berlin.
Local media suggest two German managers, Thomas Tuchel and Julian Nagelsmann, could be in the frame to replace the Italian.
Tuchel was let go by Borussia Dortmund at the end of last season after differences with the club’s management, while 30-year-old Nagelsmann is currently in charge of Hoffenheim.
Earlier this month, Bayern lost 2-0 at Hoffenheim and then relinquished a two-goal lead at home to Wolfsburg to draw 2-2 before Wednesday’s bruising loss at the Parc des Princes.
Facing criticism from the fans and the media for his failure to accommodate Thomas Mueller, Ancelotti’s relationship with the likes of Robert Lewandowski, Arjen Robben and Franck Ribery was also reported to be under strain.
The defeat in Paris was Bayern’s heaviest since losing 3-0 away to Barcelona in the Champions League semi-final first leg in May 2015.
Bayern are currently third in the Bundesliga table after six games, three points behind leaders Borussia Dortmund, before visiting Hertha Berlin on Sunday.
Ancelotti led Bayern to a fifth consecutive Bundesliga title last season in his first campaign in charge after succeeding Pep Guardiola at the Allianz Arena.
However, the Bavarians lost to Real Madrid in the quarter-finals of the Champions League and to Dortmund in the semi-finals of the German Cup.