Jenkinson spent the day with Roy Hodgson's team and joined in with training at Arsenal's London Colney training ground earlier today.
The 20-year-old will not travel with the England squad to Krakow on Monday as they prepare to face Poland in a crucial World Cup qualifier in midweek.
Hodgson has previously admitted that the Gunners right back is close to a full international call-up.
He said: "Kieran Gibbs, like Jenkinson, has started very well for Arsenal.
"On this occasion, we decided to go with him and keep Jenkinson up our sleeves, but he'll be very much in our thoughts when it comes to the next friendly match.
"He's only 20 and it's nice to temper things a little bit, but he wouldn't be out of place in the squad."
Jenkinson has taken full advantage of an injury to Bacary Sagna to become an ever-present member of the Arsenal backline in the Premier League so far this season.