Allan arrived at Liverpool in 2015 from Internacional for £500,000 but has been unable to gain a work permit to play in the Premier League.
He was subsequently sent out on loan to Finnish side SJK and Sint-Truiden of Belgium before joining Hertha Berlin last summer.
And while Allan has struggled for minutes with the Bundesliga side this season, they are keen to keep him beyond this summer.
Allan Rodrigues de Souza has been out on loan at Hertha Berlin this season
Jurgen Klopp has previously expressed his admiration of Allan
Hertha Berlin's sporting director Michael Preetz hinted to German magazine Kicker that he is confident that Allan will remain in Germany next season.
"We must and will discuss it with Liverpool," Preetz said.
Jurgen Klopp has previously expressed his admiration for Allan after first seeing him in training.
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Zlatan Ibrahimovic (Manchester United)
Klopp told Liverpool's official website in March last year: “When I came here, one or two months later Allan was here and I said ‘who is this?’
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“[The response was] ‘He is a player for us and the week before he became a champion in Finland.’
“I thought interesting – why didn’t he play here? I was told ‘because it’s not possible."
“And then I started learning about the FA rules and things like this. I saw him in training and I thought ‘oh my God, what can we do to keep this boy here and bring him into the line-up?"