Allen has a year left on his current contract and was named in Uefa's official Euro 2016 team of the tournament as Wales reached their first semi-final at a major competition.
Having started only eight Premier League games last season, the 26-year-old has yet to discuss a new deal.
"We will find a solution but it's not done," Klopp told BBC Radio 5 live.
"Obviously Joe Allen is a good player. We never doubted this. He played a good European Championship, like the whole Welsh team.
"We have to make decisions, we have to find solutions. We have to talk to the player, ask the player and think about our situation. That's how it works."
Allen joined Liverpool from Swansea City for £15m in 2012.
The Reds rejected an enquiry from the Welsh club about re-signing their former player on loan in January, and it is understood the Swans are still interested in Allen.
Manager Jurgen Klopp says Liverpool are eager to resolve the future of Wales midfielder Joe Allen.