The 33-year-old is currently without a club after being released by Steve Bruce at West Bromwich Albion, where he scored three goals in 15 appearances.
Carroll spent the first-half of last season at Reading after leaving the Magpies for the second time last summer.
The Daily Mail reports that Gateshead-born striker will undergo medical tests with a view to signing a contract.
Brugge were crowned Belgian Pro League champions last season and as a result automatically qualify for the group stage of the Champions League.
Carroll progressed through the Magpies academy before sealing a £35million move to Liverpool in 2011.
Eighteen months later, the striker joined West Ham United, with his once promising career hampered by injuries.
Carroll has been capped by England nine times.