Lukaku’s agent is understood to be in line to meet with Everton’s major shareholder Farhad Moshiri.
His current contract, signed when he joined from Chelsea for a club-record £28m deal in July 2014, is worth around £75,000 a week to the 23-year-old.
It is believed the new deal would see him earn around £100,000 a week.
Lukaku is under contract until 2019 but optimism is growing that he could now be close to agreeing an improved new deal, which would be a major boost to Ronald Koeman as he prepares to rebuild his squad.
Everton boss Koeman told Lukaku, who has scored nine goals in 15 Premier League games this season, last summer that he would not be allowed to leave despite interest from Juventus and former club Chelsea.
But Koeman has also suggested the Belgium striker will have to leave to fulfil his potential.
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