Wilshere, who joined the Hammers last summer, was restricted to only eight Premier League appearances in 2018/19 due to injury.
"I trained with him a lot and came through the system with him at Arsenal," Wilshere told West Ham's official website.
"He was just about to break into the first team and then he picked up a freak injury.
"He's a difficult person to play against and likes to put his foot in. I'm sure he will do so again, even if it's pre-season.
"It's nice being back around the team and away with them here in China.
"There is a lot of quality in this team, especially in the midfield area, so it's down to us as individuals to show the manager in training and in games that we should be playing."
Wilshere has been a popular figure among local fans during the Asia Trophy and has been struck by the generosity and warm welcome afforded him by the locals.
"I've been to China before and the people and the fans have always been good to me," he said.
"They've been giving me gifts for me and my children and I'm very grateful for that."
Premier League Asia Trophy matches
Wednesday 17 July, Nanjing Olympic Sports Center
Newcastle 0-4 Wolves
Man City 4-1 West Ham
Saturday 20 July, Hongkou Football Stadium, Shanghai
Newcastle v West Ham, third/fourth place playoff, kick-off 17:00 (10:00 BST)
Wolves v Man City, final, kick-off 19:30 (12:30 BST)