The English midfielder will return to his old stomping ground for both teams' third fixture of the Premier League season this Saturday, having joined the Hammers following the expiration of his contract in June.
And speaking ahead of the clash, Pellegrini claimed to have no idea how Arsenal could let a player of Wilshere's quality leave.
"I played here three years against Arsenal, and before that with Villarreal in the Champions League," the Chilean said, via Goal.
"Jack was always a very good player. I don't know the reason why he finished his contract with Arsenal.
"I don't know why Arsenal allowed him to come here."
Wilshere joined the Gunners in 2001 at the age of nine and played in their first team for 11 years, racking up 125 Premier League appearances under Arsene Wenger. The North Londoners are now being led by Unai Emery, who expects the player to receive a warm reception when he returns to the Emirates this weekend.
"I spoke with him for 15 minutes here in Colney before he left," the former Paris Saint-Germain boss revealed.
"The first thing for me is I have respect for his career here. And then, he chooses what the best was for him in his future.
"It's for that, on Saturday, I know that here the supporters like him and have this respect also. I think there is a good reception for him here.
"Then we are going to play and we are going to think after that, for us to win. But, I [hope] the best for his career."