Oxlade-Chamberlain's participation in Brazil was put into serious doubt when he picked up a knee problem during England's 2-2 friendly draw against Ecuador in Miami on Wednesday.
|2/1||England are 2/1 with William Hill to beat Italy in Manaus on June 14|
With the team arriving in Brazil on Sunday, England's first full training session took place on Monday and Oxlade-Chamberlain was involved, doing numerous running exercises in a bid to be fit for the group stage.
England are in Group D alongside Costa Rica, Uruguay and Italy, and although an appearance against Cesare Prandelli's men on Saturday looks unlikely, Wilshere is hopeful that Oxlade-Chamberlain can feature later on.
"Alex looks well," said the 22-year-old. "[On Monday] he was straight-line running five days after getting a meniscus strain.
"It helps [that] he's young because the body heals [quicker] when you're younger and what also helps is that he's got 24-hour treatment.
"Sometimes when you're back at a club, injuries can take a bit longer to heal because you're not getting treatment all the time, but here he's got treatment when he wants it – that was a big part of him staying here.
"Hopefully we can get him training over the next few days and get him ready for the tournament. He's got a great attitude and loves football.
"He had a knee injury at the beginning of the season which was worse than this one and he came back from that well and looked good and I think that was another factor in him staying here.
"We've seen him come back before and he's fresh as well – he's only played six months so hopefully we can get him back in the next couple of weeks."
In the build-up to England's World Cup campaign, there has been much discussion regarding the presence of a significant number of younger players, but Wilshere is adamant that there is a healthy blend of experience and youth.
"We've got a great squad – young players, experienced players and a few that are in the middle," he added.