The 26-year-old Italian international has been in excellent form this season, netting 11 Serie A goals.
His performances have seen interest in his signature spike, with Juventus in particular keen on a summer deal.
Torino are desperate to keep hold of their man, with speculation suggesting that talks surrounding a new contract are on-going.
However, the player himself is thought to be ready to leave in search of European football.
This has alerted the Premier League sides, who are all believed to be monitoring the situation closely.
United have been strongly linked with the versatile forward for some time, with reports having suggested that David Moyes sees him as s good addition in what looks likely to be a busy transfer window for the Premier League champions later this year.
Arsenal have also found their name aligned with Cerci in the gossip columns, while Tottenham, Liverpool and Chelsea are other outfits in the mix.
The former Fiorentina star has endured a turbulent career so far, but has been playing some of his best football in recent times with Torino.