Heskey, 36, is a free agent after a two-year spell in Australia with Newcastle Jets, but opted not to team back up with Kavanagh.
Kavanagh, who played in the same Wigan team as Heskey, told the News & Star: "I tried to get Emile in.
"I played with him at Wigan and I know what he is all about.
"Unfortunately he turned it down as I think he wants to be playing in the Championship or going back abroad."
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