According to The i Paper, the 24-year-old France international has emerged as a potential target following his impressive performances for the Cherries.
Truffert's form recently earned him a France recall, having made his international debut in 2022 before waiting until last month for his second appearance.
The Red Devils’ disappointing start to the season has intensified scrutiny of their summer recruitment, with the failure to sign a left-back reportedly acknowledged internally as an oversight.
Newcastle United's Lewis Hall remains a priority target, although Truffert, who previously represented Rennes, is also under consideration.
The French defender has been on United's radar for some time, but any January approach could face competition from other interested clubs.