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The Italian joined Liverpool last summer for £12.5million and had been the only addition to the squad that Arne Slot inherited from predecessor Jurgen Klopp.
However, Chiesa struggled for minutes during his first season in England, making just 14 appearances across all competitions.
In the Premier League, the ex-Juventus ace featured six times, managing a combined total of 104 minutes and being named in the starting XI only once.
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It led to Chiesa being left out of the Italy squad, with rumours a return to Italy could be about to follow this summer, just 12 months after he put pen to paper on a Premier League switch.
Now, with less than a month until the new Premier League season kicks off, even more doubts surrounding Chiesa's future have surfaced.
The Athletic are reporting that Chiesa hasn't been included in the Premier League champions' 29-player strong squad for their pre-season tour of Japan and Hong Kong.
It's claimed by the outlet that the official reason is that Chiesa is suffering with a fitness problem and is being assessed in Merseyside instead.
Read more: Liverpool 'line up another £100m transfer' but face 12-month delay to do deal
Federico Chiesa spent most of his first season at Liverpool on the bench (Image: Getty)
However, it's believed that Chiesa did feature for Liverpool during a behind-closed-doors friendly against Stoke City this weekend, which the 20-time champions won 5-0.
He has only played 25 minutes [at that point in the Premier League].
He needs more defensive phase.”
Elsewhere, Liverpool are believed to be closing in on a deal for Hugo Ekitike, after an agreement was reached with Bundesliga side Eintracht Frankfurt.