The Daily Star says Kenwright made it clear to David Moyes not to raid the Toffees squad before allowing him to succeed Sir Alex Ferguson as United boss.
Baines, 28, has not asked to leave Goodison Park and is said to feel 'awkward' about the situation.
His representatives went to ground yesterday and refused to discuss Baines' immediate future.
Kenwright said: "Leighton is under contract and I've told David not to come back for him."
But Kenwright knows he could be powerless to stop one of his prize assets from going to United.