The undisclosed offer, beleived to be around £2.5million, will see the Latics making a near £2million profit on the £750,000 they paid Motherwell for the striker turned midfielder six years ago.
Gers boss Walter Smith hopes to conclude the deal in the coming days in time for big Lee to join them for their pre-season tour of Germany.
McCulloch joined Wigan during their Division two days, and has climbed through the divisions as one of Wigan's most important players.
In 241 appearances he scored 46 goals, most from the left-flank.
His departure leaves Leighton Baines as the only surviving member of the team which won promotion from the old Division two.
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