The News of the World says Goodison chairman Bill Kenwright has assured manager David Moyes that there has been no official bid for Rodwell, whose future might well lie in the heart of defence.
But Chelsea are putting together a player-plus-cash package that would value the England Under-21 player at around £16m.
In their financial situation - Kenwright is still struggling to attract a major investor as the club's stadium plans remain in limbo - Everton would have to consider any extravagant offer for Rodwell.
But it appears that Rodwell will not put the club in that position.
And the only effect a bid from Chelsea will have is to give Rodwell's advisers leverage to improve his current contract.