The former Hammers boss has been guaranteed a sizeable transfer kitty by Stadium of Light chairman Ellis Short and sees the defence as his first priority.
Tomkins, 26, fits the bill according to the Daily Star who suggest that a fee of around £10 million could clinch a deal despite the player signing a five year contract back in February.
Allardyce is also expected to move in on out of contract former Hammers captain Kevin Nolan and Morgan Amalfitano, 30 – whose Hammers’ contract was cancelled this week by mutual consent after a bust-up with boss Slaven Bilic – could also interest him.
Robson, who played in the same Sunderland side as Allardyce in the 1980/81 season, said: “If anyone can keep Sunderland in the Premier League, Big Sam can.”