The People says Hearts are asking FIFA to sanction a £4.6m 'fee' for Webster in a test case.
Webster walked out on the Scottish club to sign for Wigan 15 months ago, citing controversial Article 17, which lets players leave before the end of their contracts in certain circumstances.
But FIFA fined him £625,000 for making the move. However, Hearts are not satisfied and a final FIFA decision will be made next month in the biggest case since the Bosman ruling changed football.
If Wigan have to cough up it will be a sensational twist, especially as the player has since moved on to Rangers. Webster - currently on loan at Ibrox - is still registered with Hearts until the dispute is settled.
Some of the biggest stars around are waiting for FIFA's ruling as it will affect every player who has a year left on their contract.