Rincon was a summer transfer target of the three Premier League clubs but no official bid was made as the Venezuelan star was involved in contract talks with the Bundesliga side.
However the 25 year old was not impressed with the contract on offer and has vowed to leave the club in January unless he is offered a superior deal.
The confident playmaker is out of contract in the summer and if a deal cannot be thrashed out before January then Hamburg will have little option but to listen to cut price offers for their star man, with the Premier League the most likely destination.
“I love Hamburger SV. But I will not accept this offer I have received,” Rincon told Hamburger Morgenpost.
“I know all about my value to the market and if we cannot agree, I will have to go.”