The Rangers-daft midfielder posted a video on Twitter of his highlights during his time with the Gunners.
Gilmour was one of seven players to leave the club following the expiration of their contracts.
Speculation over a move to Rangers was ramped up when winger Glenn Middleton tweeted "Big things coming up..." with regards to the player.Gilmour has previously tweeted about Steven Gerrard's time and admitted his grandad wants to see him pull on the light blue.
However, he suggested no move was forthcoming with the video which displayed his composure, passing ability and composure.
Gilmour, who made two appearances for the Premier League giants, both in the Europa League, copied support service Player Centre, who produced the showeel, with a praying emoji into the tweet.
The service help players put together their football CV and can create a "bespoke video montage".
A number of Hibs and Rangers fans replied to the video calling on their respective teams to sign the player.