The Toffees are yet to make an official approach for the City duo and are yet to agree a fee with Wigan for the Republic of Ireland midfielder, who would replace Marouane Fellaini
Everton are considering a triple swoop for Wigan midfielder James McCarthy and Manchester City duo Gareth Barry and Joleon Lescott, Goal understands.
As of Sunday evening, however, the Toffees and the Latics are £2 million apart in their valuations of the Republic of Ireland midfielder.
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Elswhere, Manchester City are keen to offload Barry and will sell to the Toffees for between £2m and £3m.
They would even countenence a loan move for the former Aston Villa man, contributing 40 per cent of his £120,000 weekly wage to lessen the burden on any potential suitor.
Barry would be in line for a £1.5m pay-off should he leave the Etihad Stadium on a permanent deal, as reported by Goal on Sunday.
City have also placed a £4 million pricetag on Lescott, who has one year left on the £90,000-per-week contract that he signed upon leaving Goodison Park in 2009.
No official approach has yet been made by the Merseyside outfit for the duo, but manager Roberto Martinez was at the club's Finch Farm training ground before 07:00BST on Monday morning as he prepares for a busy day in the transfer market.
Rumours have circulated that Manchester United target Marouane Fellaini will hand in a transfer request in order to force through a move to Old Trafford ahead of the 23:00BST deadline.
Everton left-back Leighton Baines is also on the radar for Manchester United, though it has been reported that he could stay at Goodison Park.