Allen's future has been up in the air for some time.
Allen has one year left on his contract at Anfield and has been attracting interest from elsewhere, notably Swansea City and the Daily Mail had reported the Reds had put a £14 million price-tag on Wales international, who was named in the Euro 2016 team of the tournament following their run to the semi-finals.
Klopp told the BBC: "We will find a solution but it's not done.
Wales' Joe Ledley, Hal Robson Kanu and Joe Allen before the game
"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."
Liverpool manager Juergen Klopp
Allen was not among the regular starters in the big games towards the back end of last season but Liverpool have seemingly been frustrated in their pursuit of central midfield targets. Both Borussia Monchengladbach's Mahmoud Dahoud and Udinese's Piotr Zielinski have been mooted as targets. The Liverpool Echo have reported that Zielinski is holding out for a move to Merseyside though the Reds have had a big rejected.
Klopp was keeping his cards pretty close to his chest in terms of the words he used. Given that Marko Grujic has been the only midfielder who has arrived at the club this summer - following an agreement with Red Star Belgrade in January - there is a chance the Reds' boss could factor him into plans for the season.
But there is still a question as to whether he would get regular game time, especially with emergence of young midfielders at the club, with Cameron Brannagan seemingly impressing when given the opportunity. A lot will depend on what Allen wants when a decision is made.
Joe Allen scores the first goal for Liverpool