The Red Devils chief is expected to wade into the transfer market next month in a bid to bolster his options and force the Premier League champions back into the title race after a difficult opening few months of the season.
An attack-minded midfielder is thought to be a priority, with the Scot looking to inject some guile and creativity into his ranks.
Cerci has emerged as a top target, with the Italian having enjoyed an excellent start to the Serie A campaign.
The 26-year-old has already notched nine goals for the Turin outfit, and is being spoken of as one of as a potential member of the Azzurri’s squad for next summer’s World Cup.
Moyes is thought to see the former Roma man as a quality addition, and the sort of player that could link well with Wayne Rooney and Robin van Persie.
Cerci has been playing as a striker for parts of this season, but is more comfortable in attacking midfield or on either flank.
After a turbulent start to his career he has settled at Torino, but is rumoured to be open to a big move.