First of all it was an interest in Wayne Rooney. Then it was a strong pursuit of Gonzalo Higuain. Which was then followed by a month-long attempt to sign Luis Suarez.
All three names being associated with a move to Arsenal would have been enough to send the imagination of the Gunners' fans running wild, but after all three moves ended in failure, the club's supporters have been left feeling more disappointment than they would have done had they not been linked with such illustrious names.
Reports emerged late on Wednesday evening that Arsene Wenger had now turned to Real Madrid pair Karim Benzema and Angel di Maria as he looks to ease the ill-feeling at the Emirates Stadium, but is the Frenchman showing too much ambition in his search for new signings?
Arsenal have long been associated with attempting to get value for money by acquiring players from around Europe, hoping they will flourish into a world-class figure over a few seasons.
But, in theory at least, the times have changed full-circle in North London this summer with Arsenal being prepared to make a huge impact in the transfer window by making three or four significant additions.
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It must be refreshing for Arsenal's supporters to see their side linked with such players, but surely it must be questioned why the likes of Benzema and Di Maria would move to the Emirates Stadium over any other European club?
Both players will have no shortage of admirers, and if Arsenal, or another club, set the ball rolling with a realistic offer for their services, that will only spark bids coming in from a range of other teams.
That's where Arsenal could come up short once again. With Manchester United and Chelsea looking for a striker, surely they would pounce on Benzema if they were made aware that we was available?
The French striker scored 78 goals over three seasons under Jose Mourinho before he returned to Stamford Bridge, while a move to United is one that he would favour over joining Arsenal.
Their other reported target, Di Maria, has already shown an unwillingness to move to London with Spurs, so why are Arsenal interested in the Argentinean just a week or so after he declared that he didn't fancy a move to England?
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Arsenal's move for Suarez was vindicated because the player had shown an interest in moving to the club after they made a bid in excess of £40m for his signature.
But the longer that Wenger attempts to show ambition in moving for players that are unlikely to join his squad, he is missing out on targets that he could realistically lure to North London.
Marouane Fellaini was available for £22m earlier in the summer but Wenger withdrew his interest in the Belgian, while Roberto Soldado moved to North London rivals Tottenham Hotspur for £26m.
Either signing would have gone a long way to satisfying the needs of the Arsenal supporters for new faces at the club, and it would have also displayed a signal of intent to future targets that the Gunners want to make their mark on the Premier League this season.
Arsenal may have one foot in the group stages of the Champions League after their victory over Fenerbahce last night, but the longer that Wenger draws a blank with his cheque book, the more likely it is that fans will be disappointed come September 2.
Wenger has already shown his hand by stating that there will be "a lot of activity" over the next 11 days. There will inevitably be arrivals at the club, but will they be good enough to make a statement with their awaiting fanbase?