Ipswich earned promotion back to the Premier League, finishing second, 11 points off Championship title winners Coventry.
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According to The Sun, that promotion may not prevent McKenna, 39, from leaving the club, with other top flight clubs interested.
It’s understood that Ipswich don’t want to let the former Man United coach leave, but are drawing up a shortlist should it happen.
McKenna has been heavily linked with a move to Crystal Palace with Oliver Glasner set to leave at the end of the season.
Palace are hoping to lure current Bournemouth manager Andoni Iraola to the club, but face competition from Chelsea.