The Germany midfielder was a revelation at the recent World Cup in South Africa, his performances earning a nomination for the Golden Ball award and a host of top clubs chasing his signature.
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But with the 21-year-old only having one year remaining on his current deal, his immediate future remains unclear, with Bremen thought to be demanding around £20 million for his services.
Ozil recently revealed that he was focussing only on completing the final 12 months of his current contract at the Weserstadion.
However, general manager Klaus Allofs - while insisting that no bids have yet been made - refused to rule out the possibility of the starlet leaving the club should a significant offer come in from the likes of Sir Alex Ferguson or Carlo Ancelotti.
“Many clubs have expressed an interest in him, but no concrete offers have been made,” Allofs told Bild.
“If we get an offer, we will deal with it and anything is possible.”
Ozil is reportedly desperate to play his football in the Premier League and has been linked with moves to Old Trafford and Stamford Bridge.
He admitted earlier this summer that moving to England would be a dream.
“There are four or five clubs in Europe that you would have to say as a player you would dream of playing for,” he said. “Manchester United and Chelsea are two of them.
“When you are looking at moving clubs it’s impossible not to pay attention to the Premier League and even more impossible not to pay attention to Manchester United and Chelsea.
“I am a winner and, when looking for a new club, I simply look at where I can be successful and where I can win the most trophies.
“If you look at recent history of Manchester United and Chelsea then it's clear that a player can be very successful there.”
Ferguson is thought to consider Ozil as an ideal successor to Paul Scholes at Old Trafford, with both Owen Hargreaves and Anderson sidelined through injury.
While midfield trio Michael Ballack, Joe Cole and Juliano Belletti all left Chelsea at the end of last season. Carlo Ancelotti is hoping to bring Benfica's Brazilian Ramires to Stamford Bridge in the near future.
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