Scharner, 32, currently plays for Bundesliga side Hamburg but has made only one league start since moving to Germany in the summer as injuries have taken a toll.
The Austria international is keen to regain fitness and views a move to Sunderland as ideal in the short term.
His agent, Valentine Hobel, said: "Paul wants to show next season what he can do for HSV but for that he needs match practice and that would probably be at Sunderland."
Scharner made over 200 league appearances in England after joining Wigan in June 2006 and subsequently moving to West Brom four seasons later.
He says he now expects to complete a return to the Premier League.
"There is yet again an interest in my services from a club in the Premiership," Scharner told Hamburger Morgenpost. "I expect them to put this in concrete terms in the next couple of days."
Sunderland manager Martin O'Neill confirmed in a press conference on Monday that he is hoping to strengthen his squad before Thursday's deadline.
He said: "We're hoping we can add someone else to squad if at all possible. We're still looking."