The 25-year-old’s current contract with Hamburg is set to expire at the end of the season.
Rincon has recently been strongly linked with the likes of Stoke, Sunderland and Fulham.
The South American is ready to leave Hamburg unless they increase their contract offer.
“I love Hamburger SV. But I will not accept this offer I have received,” he told Hamburger Morgenpost.
“I know all about my value to the market and if we cannot agree, I will have to go.”
Hamburger SV general manager Oliver Kreuzer looks unwilling to increase his offer.
“Tomas Eduardo Rincon has been handed a good contract offer. I don’t have a queasy conscience. Either he is accepting it. Or he does not.”