The 25-year-old Venezuelan is out of contract at the end of the season and turned down the latest offer of a contract at the Imtech Arena, alerting a host of clubs to his availability.
But the player's legal representative, John Sorzano, believes his client has his heart set on a switch to the English top flight, with Everton, Fulham, Swansea and West Brom rumoured to be interested in signing him.
"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 representative, Oliver Ward of ITM Sports, believes Rincon could prove to be one of the signings of the January transfer window if he moves on.
"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."
Rincon has made 93 Bundesliga appearances for Hamburg since making his debut in 2009.
