Lukaku, who scored 25 Premier League goals last season, is keen to leave Merseyside in order to play in the Champions League and fight for titles, but Everton have no interest in parting with their coveted attacker, whom they value at £100m.
Chelsea have long been interested in Lukaku, who endured an unsuccessful spell at Stamford Bridge a few years ago. Manchester United have been monitoring the 24-year-old for a number of months but are seemingly more interested in Real Madrid forward Alvaro Morata, who they are edging closer to signing.
Despite their well publicised pursuit of Morata, Mariner, who also played for Ipswich Town and Portsmouth, says Manchester United have tested Everton's resolve with a bid for Lukaku, along with Chelsea, but Ronald Koeman's men are determined to keep the Belgium international or at least hold out for a fee that matches or comes close to their £100m asking price.
"My mate is now the sporting director at Everton," he told ESPN, relayed by Football365. "I had a good chat with him and they're going to spend a lot of money this summer.
"They feel as if it's time they broke into that top four, it's a big ask but that's what Ronald Koeman and the staff want to do.
"They've had bids for [Romelu] Lukaku, mainly from Manchester United and Chelsea. It's a lot of money, I personally wouldn't be paying that sort of money. They think they can hold out for it but they've already added to the squad.
"It's going to be very, very interesting to see if they improve and I think they will improve."
Everton have been uncharacteristically active in the transfer market this summer. The Blues have already welcomed Davy Klaassen, Henry Onyekuru and Jordan Pickford to Merseyside and are expected to add to the former Ajax, KAS Eupen and Sunderland stars with Michael Keane, Sandro Ramirez and Cuco Martina, who is available on a free transfer after leaving Southampton.
Everton have also let a number of players leave Goodison Park this summer; Gerard Deulofeu and Tom Cleverley have joined Barcelona and Watford respectively, while Ivorian forward Arouna Kone has been released.