The 30-year-old spent last season on loan at Marseille and appears to have no future at Loftus Road, especially on reported wages of £70,000 a week, after their relegation to the Championship.
But his salary has put off the French club from making a move to sign him permanently and McKay is exploring other options in an attempt to find a new club.
Huyton-born Barton supported the Toffees as a boy and has this morning tweeted "Once a blue.." and his agent admits they have approached new manager Roberto Martinez about an opportunity.
"Obviously his package with QPR is pretty big for Marseille's terms really," McKay told talkSPORT.
"Joey said there was only one club he would make a sacrifice for and it would be Everton and I made that call to Martinez.
"That is the club he loves. I have approached them and said Joey would love to have Everton on his CV. Fair play to him he said he would lose money to go to Everton - and not many professionals would do that."
McKay claims Martinez, who is in the market for a central midfielder, is an admirer of Barton.
"Roberto Martinez said he likes him as a player and he also spoke to (Martinez's assistant Graeme Jones, who loves him as a player," he added.
"Anything can happen in football. It could happen."
Martinez and the rest of the Everton squad are currently in San Francisco where they will kick-off their pre-season games in the United States tonight against Juventus in the International Champions Cup.
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