Brian McDermott is supposedly a long-time admirer of the player.
The 31-year-old, who netted 10 goals for the Tigers last season and was named the fans' player of the year, has already attracted interest from Leicester this summer, with Hull's owners thought to have rejected an offer.
Koren's agent, Zoran Krneta, claims Reading boss McDermott is also chasing the Slovenian as he looks to strengthen his squad following their promotion to the top flight, having unsuccessfully tried to sign him six years ago when he joined West Brom from Norwegian club Lillestrom.
But Krneta says the midfielder will return to pre-season with Hull and meet new manager Steve Bruce before making a decision on his future.
"I cannot tell you anything right now as it is early days, but there has been a long-term admiration by Brian McDermott for Robert," the agent told the Hull Daily Mail.
"He tried six years ago to buy Robert, but he joined West Brom.
"Robert is a player Brian knows very well, but the circumstances were different back then.
"I believe there is no player in the Championship who would not be attracted to the Premier League.
"Obviously, if there was an offer from Reading then that would be something Robert would think over seriously.
"But Hull have just appointed a new manager and I am sure Robert will want to come back from his holiday and see what happens."