The Chile international moved to the Emirates Stadium last summer for around £32m after the Gunners beat Liverpool for his services.
Sanchez has since become Arsenal's key player, ahead of £42m record signing Mesut Ozil.
Even though the former Barcelona star is not a number nine, he has provided seven assists while scoring 12 goals in the first 21 Premier League games of the season, just three fewer than top scorer Diego Costa, with Aguero on 14.
Following his latest brace – with one assist – during the impressive 3-0 victory over Stoke City on Sunday 11 January, the Chilean star is starting to be being touted by some bookmakers as a Player of the Year award candidate, alongside Chelsea trio Eden Hazard, Costa and Cesc Fabregas, and City's Aguero.
With the Argentina striker missing a month of Premier League action due to injury, Pellegrini has claimed Sanchez is currently the best player in the top flight.
"Every game I see him making a great effort, showing great commitment, ambition and the maturity needed to keep improving year after year. I'm happy for him because at this time he is the best player in English football," Pellegrini said to AS.
"I always thought [he was going to be world class]. The only thing you could criticise him for before was that he didn't score enough goals. He wasn't a scorer. But he has improved this a lot in the last two campaigns."
The Arsenal star scored 19 La Liga goals for Barcelona last season even though he was overshadowed by Lionel Messi and Neymar.
Pellegrini added: "Alexis has progressed in recent years. His spell at Barcelona has been very useful for him as well as sharing a team with great players."