The London Evening Standard says McKenna has welcomed news that he is under consideration as Chelsea seek a new manager after Mauricio Pochettino's departure this week.
McKenna has just led Ipswich to back-to-back promotions, taking the Tractor Boys into the Premier League for next season.
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He won the League Managers Association manager of the year award this week - ahead of Manchester City boss Pep Guardiola.
McKenna, 38, has a deal with Ipswich to 2027. His club are expected to demand 4m in compensation should Chelsea come calling.