A number of media outlets claim the Red Devils have turned their attention towards the 25-year-old Belgian, having finally admitted defeat in their attempts to lure Barcelona's Cesc Fabregas to Old Trafford.
But Martinez denies that United have launched a bid for Fellaini, and having played in Everton's defeat against Valenica in the final game of their US pre-season tour, the ex-Wigan chief is focussed on preparing for the new Premier League season - with Fellaini very much a part of his plans.
"There are no bids," the Liverpool Echo quoted him as saying. "When you read that someone is interested in someone, it doesn't mean there is a bid on the table.
"Marouane has been working really hard. Leighton Baines has been working really hard for the team and that's all that matters."
Baines is another name to be linked with a move to Old Trafford, but Martinez is refusing to take any notice of the intense media speculation, with the transfer window coming to a close at the end of this month.
"Headlines in the media happen at this time of the season unfortunately but it won't distract me from the work we have to do. I'm not bothered at all.
"It is speculation in the media and you'll never stop that. I've said from day one as a manager you only concentrate on working hard."
Martinez is more than happy for his star players to be linked with high-profile transfers, and takes such links as compliment and acknowledgement of his player's ability.
"I don't mind having my players grabbing headlines. That's a good story because it means they've been doing well and performing well.
"I'm only concentrating on having as strong a squad as possible for the start of the season. That's all my concern is."
The Spanish tactician would loathe to lose Fellaini to United, particularly with the 2013/14 season just around the corner.
However, should David Moyes return to Goodison Park with a significant bid for his former charge, then Everton, Martinez and Fellaini may struggle to reject the overtures of Manchester United.