After achieving Premier League status with back-to-back promotions, McKenna is a target for top-flight clubs.
The former Manchester assistant coach is being linked with managerless Brighton and Chelsea.
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But The Sun says Ipswich hope to convince McKenna to stay with a new contract worth FOUR TIMES his current deal - which runs to 2027.
The new offer tabled is worth 5m-a-year and for four years.