England are due to leave 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.
Leicester are reportedly in the process of offering the 29-year-old, who signed a new three-year contract in February, an improved deal of their own.
Vardy joined Leicester from Fleetwood for £1m in 2012 and helped the Foxes to the Premier League title last season, scoring 24 goals.
