Now that Jamie Vardy is going to reportedly wait until after the European Championships to decide on whether to join Arsenal, Arsène Wenger should take the time to think through whether he really wants Vardy. As a quickly done deal with a set price, £20m, Vardy sort of made sense, in that it wouldn't be a complicated deal and would give Arsenal the cover they need upfront following Danny Welbeck's injury sustained last month. But Vardy's decision to delay his move means that the deal has now become more complicated, and also means that Arsenal are still in the market for attacking additions. In short, they should take this opportunity to move on, leaving Vardy without a decision to make.
There are several reasons why Arsenal should move on from Vardy, but of primary concern is that he wouldn't fit into Arsenal's style of play. Arsenal did poorly last year not because the style of football is a bad style, but rather because they were bad at it. With the addition of Granit Xhaka, Arsenal should be better at a possession-based game, where the goal is to build play. But that is not only the goal; it is also the reality. Arsenal cannot sit back and counter-attack against most of the teams in the Premier League because they sit back; therefore, Arsenal have to be the proactive team, rather than reactive. At Leicester, Vardy thrived because he was able to run into space, as teams felt that Leicester were a side that had to be attacked. Vardy might struggle against teams that sit back; indeed, he did for Leicester towards the end of the season (more on that later), and touched the ball 8 times in 66 minutes for England last Thursday. Some have pointed to Vardy having to play out wide, but that was only when England were out of possession, and against a Portugal side that defended in a deep block, Vardy's movement was non-existent. The way to break these sort of teams down is the ability to quickly play one-twos with other attacks, and that simply is not Vardy's game; his game is about power and pace, and while that's all very well, a degree of subtlety is required, which is why Alexis Sánchez is far better suited for Arsenal than Jamie Vardy.
There is also reason to believe that Vardy's season, as incredible as it was, was a one-off. One should be suspicious of any player who has a breakthrough campaign at age 29, especially when the underlying numbers point to it being an aberration. Of Vardy's 24 goals, 15 came in the first half of the season, with Vardy only scoring 9 times (with 3 penalties) in 2016--that is, the same number of non-penalty goals as Olivier Giroud, whose 2016 was very, very poor. Furthermore, he is not exactly more clinical than Arsenal's current strikers, Theo Walcott and Olivier Giroud, and barring 14 games, where Vardy set the record for consecutive games scored, Giroud converted a higher percentage of his shots (15.8%) than Vardy ever has in the Premier League.
So where does that leave Arsenal? There is a need for a striker, because of Danny Welbeck's injury, but Alvaro Morata looks too expensive. Daniel Sturridge should remain a pursued option, but Arsenal should also not turn their back on Theo Walcott. Walcott played well as a striker at the beginning of last season, and his poor form came after being played on the left, which he is not suited to. He only played upfront once more after October, at Old Trafford, and it is fair to say that by that point, Arsenal's midfield had lost all structure and effectiveness. That is not to excuse Walcott, but one of the reasons for Vardy's success at Leicester was the functioning midfield; now that Arsenal will again have a functioning midfield following the addition of Grantit Xhaka and the banishing of Francis Coquelin to the bench, Walcott may again be effective up front, as he was in the 3-0 demolition of Manchester United. Furthermore, Arsenal can find goals from elsewhere: Henrikh Mkhitaryan is a goal-scoring wide player, and with Xhaka in the side, Aaron Ramsey can not only be restored to his preferred central midfield role but can also have it be a functioning role; therefore, one can reasonably expect 10 or so goals from him.
Arsenal should remain on the lookout for a striker, but with Vardy now wanting more time, Arsenal should move on from him, and sort out the other needs of the squad: a wide attacking player, and a centre back, and creating a functioning base and game plan. Those are all more important than Jamie Vardy, who is not a player for who you delay building a side.