The Senegal international appears destined for a move to the Premier League in the near future.
The Mirror report that scouts from five top flight sides - Everton, Tottenham, Swansea City, Bournemouth and Aston Villa - were in attendance to watch the Ligue 1 side go up against Liverpool in the Europa League last week, with the Senegal international being the main focus of their attention.
They would undoubtedly have been impressed with the 25-year-old, who got on the scoresheet at Anfield, but could not prevent his side from losing to the Reds.
Like the game against Jurgen Klopp's side, Saivet has stood out for his club this season despite the French outfit's struggles. The midfielder has been a rock for the side, but has been unable to prevent the club's poor run of form which has left them languishing in the bottom half of the league table.
The Mirror suggest that he will be available to move on in January for just £3.5m, and it appears that that price has caught Arsene Wenger's eye.
Francis Coquelin's injury - as well as the club's subsequent results since he limped off against West Brom - has highlighted the need for the north London side to add some further depth in that area of the field. Saivet's pace, power and strength would make him the ideal candidate to act as the enforcer in the Gunners side.