Chelsea have been pushing hard to sign the 21-year-old winger despite Everton rejecting their opening bid last week.
The Toffees have been desperate to hold on to a player who has progressed through their academy but it seems they are fighting a losing battle.
Chelsea have tabled a second bid worth £50m plus another £10m in add-ons to ramp up the pressure on Everton and Gordon is now pushing for the move.
It has been claimed that during talks with Lampard he informed the Everton boss that he wants to move on from Goodison Park this summer.
The winger is now actively pressing for a move to Chelsea with the Blues confident that Everton will accept their second offer.
The 21-year-old wants to play Champions League football and believes he has a better chance of being in the England World Cup squad if he is at Chelsea.
Chelsea are not expecting any problems in agreeing on personal terms with Gordon if Everton accept a fee.
However, an agreement is not imminent and the chance of the winger staying put at Chelsea has not been ruled out.
Everton remain reluctant as they believe that they do not have enough time to find a replacement for Gordon.
