Reports have claimed that Henderson is eager to return to the Premier League after just half a season with Al Ettifaq.
The 33-year-old England international's move to the Saudi Pro League last summer came as a surprise, with the Reds' not planning to offload their captain as part of the midfield rebuild.
As well as forcing a chance in Liverpool's squad planning, the £12m transfer was not without controversy, with Henderson previously a prominent advocate from within men's football for LGBT+ rights. Homosexuality is illegal in Saudi Arabia.
In a now infamous interview with The Athletic, Henderson insisted the challenge of developing football in Saudi Arabia was what attracted him to the project. However, according to a number of recent stories, the England international has struggled to settle to the lifestyle in Dammam. Meanwhile, on the pitch, Al Ettifaq are in poor form and have not won a game since October.
The Steven Gerrard-managed side have reportedly averaged gates of just 7,800 so far in 2023/24.
The reports follow rumours that Roberto Firmino, too, is seeking an exit from the Saudi Pro League, having signed for Al Ahli last summer.
Asked about the speculation surrounding Henderson, following the FA Cup win over Arsenal, Klopp shut down a question that his former captain might return to Anfield – but admitted he had been in contact with his former captain.
"Did Hendo have a press conference and say [he wants to leave] or what?" Klopp said.
"So it is just written?
"That means for me it is not existing. He hasn't called me. We spoke actually but not about that but I really have nothing to say about that."
Liverpool reportedly have a 'healthy' sell-on clause if Henderson is allowed to leave Al Ettifaq for a return to England.