Barry will reportedly scoop a £9million jackpot by making a permanent move to Everton on a permanent basis.
The veteran midfielder, 33, spent last season on loan at the Toffees from parent club Manchester City - and he has now been offered a three-year, £60,000-a-week deal at Goodison.
His City contract is now up but, according to The Sun, Everton will still pay a £2m "transfer fee" as part of the conditions of his original loan deal.
This means it will cost Everton around £11m to land Barry full-time but manager Roberto Martinez is understood to have said he would consider this money well spent.
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