Manager Steve Bruce held talks with the 28-year-old Schalke star in January but failed to strike a deal as the player was chasing £3.5m a year.
Bruce hoped to be in a better position next month with Kuranyi available on a free transfer but Dinamo's offer will make it difficult for him to compete.
High demand: Sunderland are one of several clubs in the hunt for Kevin Kuranyi
Fenerbahce have also reportedly offered £100,000 a week but Kuranyi is not keen on Turkey, while Juventus have also expressed an interest.
Meanwhile, Sunderland midfielder Bolo Zenden is yet to decide whether to take up an offer to stay for an extra year.
Zenden, 33, said: 'I am still thinking about it.'
Bruce is still keen on Paraguay international Cristian Riveros and Udinese's Simone Pepe.
Kilgallon frustrated with lack of first-team opportunities at SunderlandPompey in good company - Premier League's most pointless clubsTHE LIST: Sportsmail's top 50 signings of the season - Nos 30-21Hutton doesn't want Spurs return as defender is loving life at SunderlandSUNDERLAND FC