The Blues are trying to convince him to stay at Goodison Park, amid interest from Chelsea.
Manchester United's Eric Bailly in action with Everton's Romelu Lukaku
The Belgian international has been linked with an exit for several months after his impressive performances last season.
Indeed, both the player and his agent has widely discussed how he wants to play for a Champions League club next season.
Manchester United's Michael Carrick in action with Everton's Romelu Lukaku
Everton are not keen on a sale though and have slapped a £75 million asking price on his head to warn off any suitors.
It appears to have worked, with only Chelsea showing interest but so far unwilling to match that price.
Everton's Romelu Lukaku in action
And according to the Mirror, they are now set to offer him wages of £135,000-per-week to convince him to stay on Merseyside.
That represents a significant upgrade on his current pay packet, with him earning £80,000-per-week at the club at present according to the Daily Star.
It remains to be see whether he will sign the deal though, with the same report claiming that he wants to return to Stamford Bridge as he believes he has unfinished business at the club following his disappointing first spell.
Everton's Romelu Lukaku warms up before the game