The 28-year-old, who has been with the Gunners since 2007 when he signed from Legia Warsaw, has made 31 appearances for Arsene Wenger’s side.
Most of his appearances this season have come in the Capital and FA Cups, although he replaced first choice goalkeeper Wojciech Szczesny following his sending off against Bayern Munich in the Champions League, and deputised for the second leg.
Were Celtic to follow up their interest in the Pole, they would likely face competition from Swiss side FC Basle, La Liga outfit Sevilla and German Bundesliga club Schalke.
Hoops boss Neil Lennon has all but resigned himself to losing England international Fraser Forster in the future, and despite Celtic lacking the funds of Basle, Sevilla and Schalke, Lennon could tempt Fabianski north of the border with the offer of regular European football.
Fabianski’s countryman Lukasz Zaluska currently plays back-up to Forster at Parkhead.