Former Liverpool player and assistant coach believes new Arsenal signing Alexis Sanchez will not be strong contender for the Golden Boot.
The SkySports pundit does not doubt the Chilean's talent, but has questions over how easy he will find it to adapt to the Premier League
In his pre-season predictions column, Thompson also cast his reservations over Manchester United striker Robin van Persie's ability to stay fit.
He said: "If he remains fit, Sergio Aguero (can win it). I can see several players having a good season, including Daniel Sturridge and Wayne Rooney.
"Robin Van Persie's tally will depend on his fitness, while Olivier Giroud will score his fair share - but will Alexis Sanchez find it easy to score in the Premier League?"
Sanchez, 25, was tipped earlier this week as the 'signing of the season' by ex Liverpool striker Michael Owen, who is not afraid to regularly write off the Gunners.
Thompson may be unfair in writing off a player who scored an impressive 19 La Liga goals for Barcelona last season, but he has never been a prolific goalscorer beyond that.
The Chilean's tally last season was the highest he has ever produced in a single league season, hitting 12 goals in his first season with the Spaniards and final year with Udinese.
Sanchez's game is clearly so much more than just scoring goals, evidenced by the 19 La Liga assists he provided over his final two seasons at Barcelona.
At Arsenal he is seen as key in unlocking the talents of Olivier Giroud, but perhaps his previous record is one argument in favour of playing him out wide rather than up front as Arsene Wenger is currently debating.