Elliott is currently on a season-long loan with Aston Villa, where the deal includes a permanent option.
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However, Villa manager Unai Emery has admitted Elliott's is not in their long-term plans and a "solution" is now being explored by the two clubs.
The issue for Elliott is that he has played for both clubs this season, meaning he cannot turn out for a third team due to FIFA rules.
As such, the one option for Elliott is Liverpool recalling the midfielder and registering him with Slot's squad.
And the Daily Express says given Liverpool's injury problems, Slot may welcome the opportunity to add Elliott for the remainder of the season.