In April the Germany international, 30, said he will leave Bremen when his contract expires in June, initially speaking of "several offers from abroad".
He later revised his expectations to playing in European competition, but he now looks set to speak to a side who lie one place below his current team in mid-table.
"I know that (Hoffenheim boss) Markus Babbel is interested, although nothing has been signed," Wiese said.
"I still have time and I will listen to all offers."
The news represents a remarkable climb-down for Wiese: Bremen were playing in the Champions League last season and, while they have struggled in 2011, their future looks brighter as coach Thomas Schaaf rejuvenates his squad.
In his time at Bremen, former Kaiserslautern keeper Wiese has won the German Cup, the League Cup, played in a UEFA Cup final and finished runner-up in the Bundesliga on two occasions.
Hoffenheim, meanwhile, have revised their ambition in recent months, with owner Dietmar Klopp looking to cut costs at the club after spending freely to establish them in the top flight.
Wiese would also not be guaranteed a starting spot as current Hoffenheim keeper, vice-captain Tom Starke, is a fan favourite.