The Guardian says McKenna is an option for Brighton - who are looking for a replacement for Roberto De Zerbi.
But Chelsea are also showing interest in McKenna as it is unclear whether Mauricio Pochettino, 52, will be staying on.
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McKenna is one of the top candidates if Chelsea decide to part ways with the Argentine coach.
Some senior figures in Chelsea's management want to keep Pochettino, but ownership group Clearlake Capital has yet to make a final decision.
Pochettino has a contract until the summer of 2025 with an option for another year.