The 25-year-old is out of contract at Hamburg and the Bundesliga side were determined to tie him down to fresh terms to ward off interest from other clubs.
However, Rincon has rejected Hamburg's latest contract offer and the German club are now ready to cash-in on the Venezuela international rather than risk losing him for nothing in the summer.
The news of Rincon's availability has alerted a host of clubs across the world with sides England, Turkey and China all chasing his signature.
The likes of Everton, Fulham, Swansea and West Brom are all thought to be weighing up moves for the highly-rated midfielder this month.
Rincon's preferred destination is the Premier League and the player's lawyer, John Sorzano, has admitted he expects some movement on the midfielder before the close of the transfer window.
"Tomas has long admired the Premier League and it's no secret that several clubs have confirmed their interest so we expect to make a more informed decision in the coming weeks," Sorzano told Sky Sports.
Rincon's UK's representative, Oliver Ward of ITM Sports, believes the South American could prove to be one of the best signings of this month's transfer window.
"A player of Tomas' track record and international experience to be available in January doesn't happen that often," said Ward.
"Tomas is moving into the prime of his career so the next move for him is very exciting."