Karl-Heinz Rummenigge says the timing has never been right for Bayern Munich to make a move for Jurgen Klopp.
Klopp last week celebrated masterminding Liverpool's first Premier League title triumph, having won the Club World Cup in December and the Champions League last season.
Bayern chief executive Rummenigge has spoken of his admiration for the charismatic 53-year-old, who the Bundesliga champions did battle with many times during his tenure as Borussia Dortmund boss.
He told Sport Bild: "I bow and say: Congratulations to Liverpool!
"Jurgen Klopp is a great coach and a very respectful person, he does not put himself above of others or talk about what a great guy he is. He is, but he does not emphasise it."
Rummenigge suggested Klopp may well have been in charge of Bayern if he was not under contract when the Bavarian giants have been in the market for a new head coach.
He added: "Whenever we've been looking for a coach, Jurgen was always under contract.
"But let's not forget that we have been blessed with other top coaches in recent years: Jupp Heynckes, Pep Guardiola, Louis van Gaal and now also Hansi Flick.
"When you're looking for a coach, the timing must be right."
Klopp is contracted to Liverpool until 2024, while Bayern head coach Flick signed a deal until 2023 after a hugely successful interim spell in charge.