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As transfer deadline day approaches, former Blackburn Rovers manager Tony Mowbray claimed the "elephant in the room" for Elliott is that his route into the first team is being obstructed by the Reds' star player, Mohamed Salah.
Elliott's future has been uncertain this summer, with the 22-year-old facing reduced playing time under Slot compared to his predecessor, Jurgen Klopp.
The 61-year-old feels that Elliott needs to be playing regular football at Liverpool; otherwise, he should express his desire for a move away to Slot.
Asked whether the winger should leave on the No Tippy Tappy Football podcast, Mowbray replied: “If I was going to advise Harvey, I would say he needs to talk to his manager.
The years start rolling by and it’s okay being a bit-part player at Liverpool but… maybe he’s waiting for Salah to move on, I don’t know.”
Another former Premier League manager, Sam Allardyce, added: “He should know whether the manager fancies him or not.
He needs to balance out how much he played for Jurgen Klopp and how much he’s going to play for Slot.
“If being a squad player’s good enough for him and he wants to stay at Liverpool, fine.
It's something I still need to review."
A transfer to RB Leipzig would see Elliott reunited with former Liverpool manager Klopp, who now serves as Red Bull's head of global football
Following his departure from Liverpool last summer, Klopp confessed his sole regret from his final season was not affording Elliott enough playing time, saying: "But if I regret one thing a little bit, it's that Harvey didn't play often enough maybe.
"Because in a very important, intense period – January, a lot of injuries - he played really good