One such player has been SC Freiburg defender Matthias Ginter.
The German international has been heavily linked with The Gunners for almost a year now - while Manchester United and Spurs were also tentatively linked with his signature.
But yesterday it seemed as though they had lost out on their transfer target - as Borussia Dortmund were reported to have completed his signing.
The Mirror reported that German daily BILD had confirmed a £6.6 million agreement between the two clubs for the talented 20-year-old to make his way to Signal Iduna Park in the summer.
It came amid claims they were also on the brink of adding Josip Drmic to their squad along with Adrian Ramos, Nuri Sahin and Ji Dong-Won for next season.
Arsenal’s hopes of snapping him up therefore seemed over.
Or not - because the club and the player himself have since refuted the claims of BILD in their pre-match press conference yesterday.
Freiburg take on Eintracht Braunschweig today and in the media hustle before the game the claims of a done deal were obviously addressed - to which Ginter personally denied:
“There is nothing fixed.”
Blunt and to the point - and certainly not denying interest is present.
But sporting director Jochen Saier was far more descriptive in how no deal with Dortmund was done at present:
"We have neither an offer from Borussia Dortmund - currently there were detailed discussions. What was reported is not true. That is all there is to it.”
The denials are genuine - but it is also fair to say that BVB might just be about to press on with a deal.
Talks are being held - and unless something drastic, like late interest from Arsenal for instance, Ginter will likely become a Dortmund player this summer.
Time will tell - but the writing does seem to be on the wall.