The 22-year-old, who was first linked with the Hoops back in April after impressing for Gabala, was expected to come to Scotland for a trial period, which never materialised.
Instead, he moved to Gabala's rivals Sabah in June 2019, signing a three-year deal.
Mustafazade made his international debut in September, and earlier this month was linked with Sunderland.
The defender was asked about Sunderland's interest in the wake of Azerbaijan's 2-0 defeat to Wales in Euro 2020 qualifying.
Post-match, he was asked: "In the last gew international matches you have performed well. Would you like to move to a foreign league?"
He replied: "Of course. I really want to [play abroad].
"Recently, Sunderland were said to be interested, I can’t name any club specifically.
"[But] they did not say anything to me, there was no official proposal.
"For my development, it will be necessary to move abroad - I am aware of this, and if the opportunity arises, then I will definitely consider it."
Celtic are well-stocked in defence, with Christopher Jullien and Kristoffer Ajer linking up well to provide a formidable central partnership, while the likes of Hatem Abd Elhamed, Moritz Bauer, Jeremie Frimpong, Boli Bolingoli and Jonny Hayes in the full-back areas.
Jozo Simunovic is stepping up his return from injury while Nir Bitton and Jack Hendry can also operate at the back.
Mustafazade is unlikely to be a primary target for Celtic but given his desire to play abroad, he could