The striker has been the subject of two offers from Stamford Bridge, with Thomas Tuchel having identified Gordon as a main target.
Sources familiar with the situation suggest an offer of around £50million would be enough to deliver a breakthrough in talks, although Everton are currently insisting the player is not for sale.
Frank Lampard is believed to see the academy graduate as an integral part of his plans, although the club’s hand could be forced should a big offer be made.
Gordon enjoyed a breakthrough Premier League campaign last season, appearing as a beacon of hope for Everton supporters in an otherwise miserable campaign. In 35 outings, the England U21 international has scored four times, including a decisive winner against Manchester United in April.
Yet Gordon has been warned by former Everton winger Andrei Kanchelskis to stay at Goodison Park for another season to help his development, just as Wayne Rooney did before moving to United in 2004.
“Gordon is a great player,” he told OLBG.
“He’s like Rooney, a young Everton player. Chelsea are interested in him. I think he should stay this season at Everton and then move to another club next season like Rooney did.
“Rooney stayed for a season or two and then moved away. If Gordon stays and wants to play with money he will be a good player, that is very important for all young players.