Central defender Rogne, who is likely to face Dundee on Sunday, has rejected a previous offer of a new deal.
"We have made him an offer and it has been refused," Lennon said. "We may go back to him with another but there are no guarantees on that.
"Obviously we don't want it to fester on. We would like to get a result one way or the other.
"Thomas is a good player, we would like to keep him around and there is a good chance of him playing on Sunday.
"He has had to be patient because Efe Ambrose, Charlie Mulgrew and Kelvin Wilson have done exceptionally well, but whenever Thomas came in he has never let us down.
"And we intend to talk to Paddy and his representatives over the next couple of months."
Meanwhile, Lennon revealed Scott Brown will find out if he requires surgery on an abductor problem early next week.
"The specialist is coming back with his prognosis," he said. "He may need surgery but we won't know that until Monday, the specialist is on holiday at the minute.
"We are expecting the specialist to say he may need surgery. If that is the case we will get it done. He is a very important player, the captain, but the squad is strong."