The Bosnia & Herzegovina striker trained with Rangers on Monday but agent Jan Bezemer reported that he has spent Tuesday with the Black Cats as he seeks a new club, following his summer departure from PAOK Salonika.
"Zlatan trained at Rangers yesterday (Monday)," said Bezemer, in remarks reported by STV. "Everything was nice and we were interested. But now another offer has come in to train at another club. Zlatan trained at Sunderland today (Tuesday) and we will now see how that works out."
He added: "Zlatan had a very good feeling about Rangers. They are a very nice club, the trainer was a good man and he spoke very well.
"Rangers want him but we have lots of interest in the player. He would like to play in a good league. The leagues in Scotland and England fall into that category."
Muslimovic, 30, has scored 12 goals in 33 caps for his country, who missed out on both the 2010 World Cup and this summer's European Championship after play-off defeats to Portugal.
Before joining PAOK he had a spell in Italy, first with Udinese - where he failed to make an impression and was loaned out to seven clubs, enjoying his most prolific spell at Rimini - and then Atalanta.