On-loan this season from Liverpool, Elliott's deal includes an obligatory permanent option set at £35m should the midfielder make 10 appearances.
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Elliott so far has played five games and the Independent says there is now discussion inside Villa about whether they want to keep him long-term.
As such, there is the prospect of Villa manager Unai Emery freezing out Elliott leading up to the January market before sending him back to Liverpool.
Watching developments are RB Leipzig, which were beaten by Villa to the signing of Elliott over the summer.