According to reports in Spain, United will be forced to stump up almost £100million in order to sign the Argentine.
United are desperate to sign a striker in January, and are reportedly looking at Martinez from Inter Milan.
The Argentinean forward has scored seven goals in 13 games this season, and is unlikely to come cheap for the Red Devils.
And Mundo Deportivo reports that the Italian side have demanded €111m [£95.6m] for his signature.
Inter paid £22.5m to sign him from Racing Santander last summer, and since then he has become one of the key members of Antonio Conte’s squad.
He was more of a bit-part player last season in his first year at the club, starting just 13 Serie A games.
But after Mauro Icardi was allowed to leave for Paris Saint-Germain on loan in the summer transfer window, Martinez has emerged as more of a starter.
Conte has viewed him as the perfect strike partner to Romelu Lukaku, who Inter signed from Manchester United when they let Icardi leave.
It was reported that Barcelona were also interested in signing the 22-year-old, but have now withdrawn from the race, per Mundo Deportivo.
United are keen to sign a new striker to provide some backup for Marcus Rashford, and have also been linked with Juventus star Mario Mandzukic.
The 33-year-old Croatian has not played a single minute for Juve this season so far, and is likely to be moved on in January.