Allardyce, 60, is back in management having taken the reins at the Stadium of Light on Friday, after Dick Advocaat left his position as Black Cats boss last weekend.
'Big Sam' arrives with the ask of taking Sunderland away from the relegation zone, which won't be an easy task, given that they have yet to win a Premier League game this season.
Allardyce will want squad reinforcements in January, and two of his former West Ham players have already been linked with moves to Wearside, with The Telegraph and The Scottish Sun reporting that Allardyce wants Kevin Nolan and Carlton Cole respectively.
Now though, The Mirror believe that French playmaker Morgan Amalfitano - another player who worked under Allardyce at West Ham - is a target for Sunderland, having been released by the Hammers just a matter of days ago.
The 30-year-old playmaker scored three goals under Allardyce last season, and was largely used as a super-sub to make an impact late in games, with great creativity and attacking threat late in games.
His release outside of the transfer window means that he wouldn't be able to sign a contract until January, but he can train with Sunderland until that point - an avenue Allardyce should consider if he is looking to reunite with the former Marseille star.