It was reported last month that Wenger had activated Vardy's £20 million release clause with Premier League champions Leicester City, but the 29-year-old England striker is waiting until Euro 2016 finishes to make a decision on his future apparently.
That being said, the French manager appears to be rather pessimistic in his pursuit of Vardy - who netted 24 Premier League goals last season - after admitting to The Standard on Sunday that the forward will most likely stay at the King Power Stadium.
However, a report from The Mirror has suggested that Arsenal fans need not feel disappointed as they claim that Lewandowski - who scored 42 goals in 50 games in all competitions last season - is a back-up option for Arsenal.
Some Arsenal fans were a touch underwhelmed by Vardy, given his age and the fact that so much of his game is based on speed, making him not much of a threat in the long term.
But 27-year-old Lewandowski is a bonafide world-class striker and his arrival would send the red half of North London into a frenzy.