According to BBC Sport, Arsenal made a bid for the England international striker at the start of the month.
BBC Sport has also reported that Arsenal have made the 29-year-old striker an offer of £120,000 per week.
It has been reported that Leicester have responded with an offer of £100,000 to convince Vardy to remain at the King Power Stadium next season.
Former Arsenal attacker Merson has suggested that the Gunners fans would not welcome Vardy now as he has taken too much time to decide on his future.
"If Arsenal come calling for you, and you don't come in the first 24 hours then you aren't signing,” Merson told talkSPORT when asked about the current situation regarding Vardy.
"I mean, you are talking about one of the biggest clubs in the world. Everybody wants to play for Arsenal."
“You sort of look at it now and you think, ‘Would the fans be happy if he went now?’” added the former England international attacker.
“Because they would be looking and thinking, ‘Wait there a minute. Why didn’t you come straightaway?’”
Vardy was one of the best players in the Premier League for Arsenal last season and was a key figure in Leicester’s title triumph.
The England international striker scored 24 goals and created 46 chances in 36 league matches for the Foxes during the 2015-16 campaign.