Various national newspapers reported on Wednesday lunchtime that, having failed to arrange a deal for Barcelona midfielder Cesc Fabregas, United have firmed up their interest in the Belgium international.
It is believed United have made contact with Everton over the possible signing of Fellaini, who has a £23.5 million buyout clause that expires on August 15.
United manager David Moyes signed Fellaini for £15m in 2008 when Everton manager and has targeted a new midfielder as a key priority this summer.
Odds comparison website Oddschecker reported a surge in bets for the move and one bookmaker (Sky Bet) makes it just 2/7 that Fellaini moves to Old Trafford.
The best price you can get on Fellaini joining the Red Devils is evens with Bet 365 but even they offer a bigger price (7/4) on the player staying at Everton. Arsenal, who have also been linked with the Belgian, have drifted out to 10/1 outsiders.
Manchester United being backed at odds on to sign Marouane Fellaini as they reportedly step up interest.
However, speaking to the official club website, Martinez said: "There are no bids.
"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 and that's all that matters.
"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'm only concentrating on having as strong a squad as possible for the start of the season. That's all my concern is."
When Moyes was picked to replace Sir Alex Ferguson as United manager, Fellaini spoke of Moyes being a "tough but great manager".
"He is a decent man, a great manager, but believe me he can be tough. If you want to win something, to create a good team you have to be hard sometimes with the players - football is like this," he told the Mirror. "He can be scary.
"I remember when I was banned after the Stoke game, he gave everyone the day off - everyone: the players, the entire staff - but I came to the training camp to do a training session with him.
"It was just me and him, and it is not easy to go into the camp to face him like that.
"I understood, because I knew I had made a mistake, but you know it's not easy when you know you have let him down. Just going in there knowing you have to look him in the eye was hard!
"He put me through a tough session... it was a full-on session, running, shooting, passing, everything and very intense, and afterwards I was upset.
"I said afterwards, 'Arggh, this is bad', but I am happy when he looked after me, so I understand."