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The youngster confronts significant competition at Anfield following the arrival of Florian Wirtz, whilst Jeremie Frimpong provides cover for Mo Salah on the right flank.
Leipzig will endeavour to persuade Elliott that they represent the ideal destination for his next career step before engaging in more comprehensive negotiations with Liverpool, reports the Mirror.
They're also expected to generate more than £70 million ($93.05 million) from Benjamin Sesko's departure, with Manchester United and Newcastle battling for the striker's services.
Last June, Elliott received encouragement from Jermain Defoe to 'get out and play' following his contribution to England U21s successfully defending their European Championship title.
Speaking on Channel 4 after Elliott's decisive brace against the Netherlands in the semi-final, Defoe commented: "There'll be a lot of clubs watching this tournament.
"We said it before, he's too good to not be playing.
Elliott helped England U21s retain their Euros crown this summer
"For him, he just needs to go out and play, get himself in a team where he's one of the main players, and just go out and express yourself and show how good you are because this performance tonight, it's amazing."
Joe Cole, also providing analysis for Channel 4, echoed his former England teammate's sentiments
For a player to come to a tournament and do what he's done, there's levels for him to go up again, and I'd love to see him playing with that kind of passion and happiness on his face every week."
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