Ashley Young, Rafael, Nani and Anderson have been told to improve or face the axe in the January transfer window.
All four have had poor starts to the season, with Nani booed off by United fans against Stoke last weekend.
Young has been dropped from the starting lineup following his performance in the derby day defeat to Manchester City last month, although he did start against Norwich City in the Capital One Cup this week.
Brazilian midfielder Anderson has failed to impress during his limited minutes, and has been linked with a return to Porto.
Although Nani signed a new five-year United contract earlier this season, the report suggests that was more down to the club's desire to retain the player's sell-on value - his contract was set to expire next summer.
As for Rafael, Moyes was reportedly disappointed with his performance in the victory over Real Sociedad in the Champions League and against Southampton in the Premier League the week before.
The Brazilian then missed out on the victory over Stoke, but returned for the Capital One Cup fixture against Norwich.
Moyes had a frustrating summer, with the club unable to secure many of its top targets. United want to ensure they don't repeat those mistakes in January, and are ready to offload a number of fringe players to free up space for new additions.