The Athletic reported earlier this week that City had seen a bid rejected by Frankfurt. His current side had placed a valuation of £67.1m but Pep Guardiola's men were only willing to pay £50.4m.
Marmoush joined the Bundesliga side from rivals Wolfsburg in the summer of 2023, netting 37 goals in 67 appearances since then.
City, who are struggling this season in their title charge, are short of centre-forward options following Julian Alvarez's summer transfer to Atletico Madrid.
Erling Haaland has started 28 matches across all competitions for City this season without competition for his place.
The Citizens have enjoyed a fruitful January window. They agreed to a deal with Lens to sign defender Abdukodir Khusanov while in a separate deal, they agreed to terms with Palmeiras to purchase Vitor Reis.
City are currently sixth in the Premier League and next face Ipswich Town on Sunday.