Burey was on the books at the Den between 2019 and 2023, when he departed to sign for Danish side OB.
The 23-year-old spent the second half of last season back in England on loan at Oxford United in League One.
He could now be returning to English football as Fleetwood are closing in on his signature.
Fleetwood were relegated from League One last season and are keen to bounce back as quickly as possible.
They see former Millwall man Burey as someone who can help in that task.
Burey, a versatile attacker, made just five appearances for Oxford in League One over the course of his loan spell.
He has struggled to make any meaningful impact during his time at OB in Denmark, with just eight outings to his name.