Iversen spent last season on loan at Preston North End and was their first-choice goalkeeper, making 46 appearances in the Championship.
He has two years left on his Leicester contract but the 25-year-old Dane is not close to making his first-team debut for the club.
Sunderland are in the market for a goalkeeper and Iversen is one of the players the Black Cats are tracking with a view to signing him.
But it has been claimed that Leicester are yet to take a decision on Iversen in the ongoing transfer window.
Brendan Rodgers is still assessing Iversen and all eyes will be on what the former Celtic manager decides.
Iversen is also keen to sort out his future.
If Leicester make a decision on him, more clubs are expected to join the queue to sign the goalkeeper this summer.
