The 29-year-old striker is set to tell the Gunners of his decision prior to flying to the national team's base for the tournament in Chantilly, France.
England depart from Luton airport at around 11:30 BST.
Arsenal have reached an agreement with Leicester and offered Vardy a four-year deal with a significantly higher wage.
Vardy is understood to still be mulling over whether he wants to leave the Foxes.
He arrived from then non-league side Fleetwood for £1m in 2012 and helped Leicester to the Premier League title last season, scoring 24 goals.
Vardy signed a new three-year contract in February and Leicester are reportedly in the process of countering Arsenal's offer with an improved deal of their own.
Jamie Vardy is expected to decide whether he will join Arsenal from Leicester City before leaving for Euro 2016 with England on Monday.