The 26-year-old is out of favour at Turf Moor despite being their joint club-record signing after completing a move from Middlesbrough last summer for a fee of £15 million.
Gibson featured in just one Premier League game all season, playing twice in the F.A Cup owing to injuries.
Burnley are keen to move him on permanently this summer, but are open to a temporary exit, and Newcastle are planning to table an offer of a loan with a view to a permanent deal.
Bruce was keen on the England international while at Sheffield Wednesday, and he reckons adding him to his squad will help boost the Magpies’ defensive ranks.
While Gibson has suffered a dip in form in the last two seasons, he remains a top player who will be motivated to work his way back to the top next season.
He is definitely eyeing returning to manager Gareth Southgate’s Three Lions’ squad ahead of Euros 2020, and Newcastle could hand him the opportunity to impress the national team selectors.
The England boss has always being a fan of Gibson’s defensive abilities and his leadership qualities, and the Toons will be sealing a huge deal if they manage to beat suitors to his signature.