The Black Cats are one of several clubs to have been linked with Graham throughout the last month and have made a formal offer for the unsettled striker, according to Sky Sports News.
Despite the player's apparent wish to leave the Liberty Stadium, Laudrup is still unsure whether a transfer will materalise before the deadline on Thursday.
He said: "It was my decision not to start him today because of all that he went through. What will happen with Danny, we will see in the next couple of days. I don't know what is going to happen.
"There are only two days left [in the January transfer window]. It's better in February to talk about what happened."
Norwich City have also been credited with an interest in Graham, who has scored seven goals in 23 Swans' appearances this season.