The Black Cats are looking to bolster their attacking options this month and Ghana international Muntari is said to be top of boss Steve Bruce's wish-list.
The striker would apparently prefer a move to London, but the North East side appear to be the most likely destination for the 26-year-old, according to his agent, Fabien Piveteau.
The Italian press have reported that Tottenham, Everton and Liverpool have all made bids for him, but his agent has refuted these claims too.
Speaking to Sky Sports, Piveteau said: "There is just Sunderland and West Ham, nobody else is in for him.
"We hope to have everything sorted shortly, maybe by Tuesday.
"He knows Sunderland is a good club, possibly not the biggest but he wants to be playing football.
"The other Ghana players at Sunderland have told him about the club which has obviously played a part."
Any deal that is completed is likely to be a loan deal, with a view to a permanent switch later on.
Bruce also appears to have Paris Saint Germaine's Stephane Sessegnon in his sights, but talks are not progressing with the Benin international, so he may turn his attentions to Borussia Monchengladbach's USA international Michael Bradley instead.