The Gunners have been linked with a move to sign the Scotland international throughout the summer transfer window so far but Arsenal haven’t matched Celtic’s valuation.
Arsenal boss Unai Emery is thought to be eager to bolster his defensive options ahead of the new Premier League season given Arsenal lack depth in their back four.
The north London side parted company with Stephan Lichtsteiner earlier this summer, Rob Holding and Hector Bellerin are still injured, while Shkodran Mustafi and Sokratis Papastathopoulos are yet to convince.
Sky Sports News reporter Solhekol has now revealed that Arsenal are closing in on a deal to sign the promising 22-year-old Celtic defender in the current transfer window.
Solhekol wrote on Twitter: “Arsenal increasingly confident deal with Celtic for Kieran Tierney is edging closer.
“Still no official third bid but talks suggest all parties will be satisfied when it’s submitted.”
Arsenal started their summer spending with the addition of Brazilian teenager Gabriel Martinelli in a £1.6m deal from South American club Ituano.
The Gunners last week reached an agreement with Saint-Etienne to sign 18-year-old defender William Saliba ahead of rivals Tottenham Hotspur.
The north London side have also signed Real Madrid midfielder Dani Ceballos on loan for the 2019-20 Premier League season.
Arsenal finished in fifth spot in the Premier League table last season to miss out on a spot in the Champions League.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news