The Athletic reported earlier this week That City witnessed Frankfurt reject the offer. His current side had set a valuation of £67.1m, but Pep Guardiola's men were only willing to pay £50.4m.
Marmoush joined the Bundesliga team from rival Wolfsburg in the summer of 2023, and has scored 37 goals in 67 matches since then.
City, which is struggling for the title this season, suffers from a lack of centre-forward options after Julian Alvarez's summer transfer to Atletico Madrid.
Erling Haaland has started 28 matches in all competitions for City this season without competition for his place.
Citizens have enjoyed a productive January period. They agreed a deal with Lens to sign defender Abdulkader Khosanov while in a separate deal they agreed terms with Palmeiras to buy Vitor Reis.
City are currently sixth in the Premier League and will face Ipswich Town on Sunday.
