Juventus are eyeying this summer, according to reports in Italy, with the Egyptian struggling to make a significant impact at the Etihad since his move from Eintracht Frankfurt.
Marmoush joined City in a deal worth just under £60m, but has not lived up to expectations since arriving in Manchester.
Newcastle United had also shown interest in the forward at the time of his original transfer from Frankfurt, but the 27-year-old may now be considered too expensive given his struggles to establish himself as a regular contributor for Pep Guardiola's former side.
Should Juventus move to test Manchester City's resolve over a potential sale, it would represent a significant change of scenery for Marmoush after a difficult opening period in the Premier League, with the Italian club hoping a fresh start elsewhere could help reignite the form that initially made him such a sought-after target.
Marmoush arrived at City with a strong scoring record from his time in Germany, having established himself as one of the Bundesliga's most productive forwards before his move to England. His struggle to replicate that output under Pep Guardiola has raised questions over whether he ever fully adapted to the demands of City's system, despite the significant fee the club paid to bring him in.
Juventus' interest comes as the Italian club continue reshaping their forward line this summer, with Marmoush's pace and versatility across multiple attacking positions seen as attributes that could translate well to Serie A, even if his time in the Premier League has so far fallen short of expectations.