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 in the north west.
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."
Former Leicester, Liverpool and Aston Villa forward Heskey returned to England last month from Australia, where he worked alongside former Carlisle striker Michael Bridges, now coach at Newcastle Jets.
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