He is the current leading scorer in England's top division with 16 goals and Leicester have moved to reward him for an excellent second season in the top flight.
Vardy's old deal does not run out until June 2018 but the new terms will represent a significant improvement in salary.
Leicester are also keen to tie down England under-20 international Ben Chilwell, another player to have attracted interest in January.
Chilwell, 19, has been regularly scouted by Arsenal and Liverpool and is regarded as one of the most promising young English players in the country.
He has less than 18 months left on his current deal but Leicester will step up negotiations in the next few weeks.
Meanwhile, Liverpool manager Juergen Klopp said he was aware of Leicester City's game plan ahead of Tuesday's trip to the King Power Stadium, but admitted that the knowledge, by itself, would not guarantee a result for his club.
Leicester, who top the Premier League table ahead of Manchester City and Arsenal, play a highly effective brand of counter-attacking football that has resulted in them losing just twice in the league all season.
Klopp and Arsenal's Arsene Wenger are the two managers to beat the Foxes, and Liverpool's German boss is a self-confessed fan of their style of play under Claudio Ranieri.
"It is a perfectly tuned team, to be honest," Klopp told reporters at his pre-match news conference.
"We all know about (Leicester's) quality ... their clear idea of their game, their clear style. It's difficult to play against, as most of the teams in the Premier League have felt when they've met them.
"The good thing with a clear plan is you know about it, so they won't change a lot -- but all the other teams knew about it too and they couldn't avoid their strengths for 95 minutes."
- Telegraph