Jürgen Klopp's side played Sporting in pre-season and the Reds boss is said to have been impressed by his display as the team's anchorman in the 2-2 draw in the United States.
And Portuguese publication Record claim the Liverpool boss is now tracking him with a view to making a move in the future.
A deal is unlikely to be done this summer as Liverpool are well stocked in midfield as he is relatively inexperienced.
Doumbia, 21, started only four games in the league last season and made another eight appearances from the bench.
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