The 21-year-old Swiss international joined Villa from SC Freiburg for €60 million in July, signing a contract until June 2031.
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Manzambi has enjoyed an impressive start to life in the Premier League, registering two goals and two assists in four appearances.
Despite growing interest from Europe's biggest clubs, he reportedly believes continuing his development under Unai Emery represents the best decision for his career.
Bayern remain admirers following his Bundesliga spell, while Barcelona have been impressed by his performances in England.
However, the midfielder is understood to be happy at Villa Park and has no immediate plans to leave.