Koeman’s future at the Camp Nou is under immense pressure following a disappointing run of results in the last fortnight.
The La Blaugrana board opted to offer their backing to the Dutchman this summer, with his current deal expiring in 2022.
However, with Koeman potentially on his way out of the club, Martinez has emerged as one of the favourites to succeed him in Catalonia.
The former Everton head coach is rumoured to have indicated his willingness to walk away from the Belgium job next month, as per reports from Goal.com, via Diario AS, if Koeman is dismissed.
The report states Barcelona will have to pay €1.5m in compensation to the Red Devils with Martinez’s contract running until June 2022.