The Foxes are looking to strengthen their goalkeeping department in the summer after failing to adequately replace Kasper Schmeichel, who joined Nice last year.
Danny Ward has stepped up to the number-one position following Schmeichel's departure, but there is some doubt whether he can be Leicester's first-choice goalkeeper for the long term.
Leicester has identified Patterson as a potential target, and they are preparing to launch a summer move for the Sunderland goalkeeper.
The 22-year-old has featured in all 38 of Sunderland's Championship matches this season, keeping 11 clean sheets.
According to The Sun, the Foxes could be willing to offer Iversen to Sunderland in a possible swap deal for Patterson.
Iversen has spent time on loan with Oldham Athletic, Rotherham United, OH Leuven and Preston North End, but he has been unable to force his way into the Leicester first team.
The 25-year-old has never featured in the Premier League and all five of his appearances for the Foxes have taken place across the EFL Cup and FA Cup this season.
Although Leicester are prepared to include Iversen in a swap with Sunderland, his wages could prove to be a stumbling block for the Championship side.
Should Leicester decide to move for Patterson, they could face competition from fellow Premier League clubs, including Wolverhampton Wanderers.
Earlier this month, Sunderland boss Tony Mowbray stated that he was keen to retain Patterson's services, but as a head coach rather than manager, he acknowledged that some transfer decisions may be out of his hands.
As quoted by the Northern Echo, Mowbray said: "I can give an opinion on anything, but ultimately, I'm pretty sure I won't be making the decisions. Ultimately, for me, the proof of the pudding will be in the eating.
"You wouldn't want to lose Dan Neil or Anthony Patterson at 21-years-old or so. You would hope that you could find a way, contractually, to secure them.
"But if the model becomes that we're going to sell players along the way, then you hope that you get the top prices for them so that there is money to reinvest back into the team."
Patterson, who is under contract with the Black Cats until June 2026, recently received his first call-up to the England Under-21 side.