The Wales star looks set to leave Anfield this summer.
Liverpool manager Juergen Klopp
The midfielder has been heavily linked with an exit after falling down the pecking order at the club.
While he featured under Jurgen Klopp last season, the German often preferred Jordan Henderson, Emre Can and James Milner ahead of him.
Liverpool's Joe Allen warms up before the match
After shining at Euro 2016 with Wales, there are a number of clubs interested in his signature and he is likely to be keen on a departure for regular first team football.
Thompson though, wants to see the Reds hold on to the Welshman this summer.
“I’d also like to see Joe Allen stay and I’ve been saying that for a long time,” he told the Daily Star.
“Has was one of our most consistent performers after Christmas and deserves a new deal and more playing time.”
Liverpool's Joe Allen in action
While Thompson would like to see Allen staying at the club this summer, it is hard to see it happening.
He is likely to find regular playing time hard to come by at Anfield next season though, with competition for places in Liverpool’s midfield stern to say the least.
The aforementioned trio is already ahead of him, while the addition of Marko Grujic add further rivalry for a starting role, making an exit even more likely.
Joe Allen celebrates with Jordon Ibe after scoring the first goal for Liverpool