Dier has only recently received his first caps for his country, but his consistent excellence in defensive midfield for Spurs has impressed.
And Jenas believes that Dier should be accompanied by his Spurs teammate Dele Alli in France.
Alli has been nothing short of a revelation for Tottenham this season, and Jenas believes that the 19-year-old could be set to star at the international tournament.
"On current form, you'd have to pick Eric Dier because he has been playing regularly for Tottenham and he has barely put a foot wrong," Jenas said.
"Dele Alli has been outstanding, but I think he'd be best used coming off the bench in the Euros and he could set the tournament alight."
Dier and Alli have been two of Tottenham’s most prominent performers over the early part of the campaign.
The pair have helped Spurs climb into the top four, and despite their rapid rises they have shown no signs of over confidence.
England kick off their Euro 2016 campaign on Saturday 11th June with a match against Russia, before they face Wales and Slovakia.