Nothing wrong with that with the Gunners' bid for the 29-year-old England international reported to be in the region of £20m which has triggered the release clause in his contract.
Vardy scored 24 goals in the Premier League for Leicester as the Foxes won the 2015-16 title.
The forward, who is currently preparing for Euro 2016, joined City for £1m from Fleetwood in 2012.
Vardy rose through non-league football after being released by Sheffield Wednesday at 16 for being too small, and was named the Football Writers' Association Footballer of the Year for 2015-16.
Since making his England debut in 2015, he has scored three times in eight internationals.
Arsenal, finished second in the league, 10 points behind Leicester, and have already signed Switzerland midfielder Granit Xhaka from Borussia Monchengladbach.
But, from England's perspective the timing couldn't have been worse. England boss Roy Hodgson came in for some criticism for allowing Vardy time off to get married thus missing the game against Australia - and the prospect of all the haedlines being about a big money move will not be good news.
With the possibility of players being involved in the Euros until mid-July any deals could have been done after that.
Vardy may well be the sort of player who won't get phased but there are plenty of examples where players subject to big money moves take their eye of the ball- literally - you only have to look at West Brom's Saido Berahino whose career is in tatters after a big money move to Spurs broke down.