The 31-year-old has long been linked with a move to the Premier League new-boys.
But Koren 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,” Koren’s agent Zoran Krneta 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.”
