Jamie Vardy celebrates after scoring the third goal for Leicester City
The BBC report Vardy is weighing up the decision, and will inform Arsenal of his choice by 11.30am Monday.
This time is significant because it is the time England fly out to France for Euro 2016, and Vardy wants his future settled one way or another before the tournament.
England's Jamie Vardy
Vardy reportedly has a four-year contract on the table, with Arsenal meeting his £20 million release clause over the weekend.
The BBC report Leicester City are in the process of making Vardy a counter-offer to stay at the club, where he is regarded as a hero.
England's Jamie Vardy in action
Vardy fired Leicester to win the title this season, scoring 24 goals in 36 games, winning the Football Writers Player of the Year award.
His dalliance with the Gunners would swiftly be forgotten by Leicester fans if he decides to stay at the club and prove his commitment, leading their first charge into the Champions League.
Leicester City's Danny Drinkwater, Jamie Vardy and Robert Huth with the trophy on the bus during the parade