De Jong's future is currently the subject of much speculation, with incoming Man United head coach Erik ten Hag said to be determined to bring him to Old Trafford this summer.
A figure in the region of £51m would allegedly convince Barcelona to sell the Netherlands international due to their ongoing financial problems.
Man United will not be able to offer Champions League football for next season, though, with the club instead battling West Ham United for a spot in the 2022-23 Europa League.
The report claims that the former Ajax youngster is owed £6m in unpaid wages due to Barcelona's ongoing financial issues, but he would be prepared to waive that figure to secure a move to Etihad Stadium.
De Jong has been a key player for Barcelona this season, making 45 appearances in all competitions, contributing four goals and five assists in the process.
"He's an important player for me, and he started every game except for a few due to rotations. But it depends on the economic situation. For me, Frenkie could be one of the club legends," Xavi told reporters.
Since arriving at Camp Nou from Ajax in 2019, he has scored 13 goals and registered 17 assists in 138 appearances for the Catalan giants.
De Jong still has more than four years left to run on his contract but is allegedly viewed by his club as a player capable of raising a high transfer fee this summer.
Offers in excess of £43m would allegedly bring Barcelona to the negotiating table, while the La Liga side would not turn down a bid of £51m, which would not be a problematic fee for Man City despite the club already committing to signing Erling Braut Haaland from Borussia Dortmund.
De Jong won the Eredivisie and KNVB Cup during his time at Ajax, but he has only lifted one trophy since arriving at Barcelona - the 2020-21 Copa del Rey. body check tags ::