The 26-year-old midfielder joined West Ham on a three-year deal in July, ending his 17-year association with Arsenal in the aftermath of Wenger’s departure.
And Wilshere has said that Unai Emery’s arrival as head coach altered his prospects in north London and convinced him it was time for a change.
“If Arsene had stayed I would have stayed because of the influence he had in my career and the trust he had in me,” Wilshere told the Islington Gazette.
“He gave me the armband and respected me a lot. So, I had pretty much agreed to stay. And then he left and that changed things.
“Arsene had said to me previously ‘stay and fight your way back into the team’. Because I knew Arsene and knew he had trust in me, I knew I could do that and fight my way into the team.
pic.twitter.com/2UdxcdyYXT — Jack Wilshere (@JackWilshere) June 19, 2018
“I knew that if I got myself fit and was training well that Arsene would put me in – and he did.
“But things were changing at the club and they were going into a new era and maybe it was time for me to leave as well.”
Wilshere, who won the last of his 34 England caps at Euro 2016, has had the start of his West Ham career hampered by an ankle injury.
He has made four Premier League appearances for the Hammers under Manuel Pellegrini, the last coming on September 1.
Wenger, meanwhile, has been out of work since leaving Arsenal but has suggested that he would be ready to return in January.
The 69-year-old has been linked with the Real Madrid job in recent times, with Julen Lopetegui seemingly on the brink after a dismal run of results.