The 27-year-old has had limited chances under Pep Guardiola this season, starting just five of his 15 Premier League games.
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With Erling Haaland ahead of him in the pecking order, Marmoush is understood to be open to leaving City in the summer.
According to Sport, the Egyptian is attracting interest from Barcelona, who are looking to sign a new forward.
Robert Lewandowski looks set to leave the Camp Nou as a free agent, freeing up some much-needed room on their wage bill.