The 25-year-old Swede, who joined the club in 2023, was sidelined by injuries and loaned to FC Twente last year.
The offer from Braga would see Celtic make a rare financial loss, having signed the player for £3m.
Fabrizio Romano reported the offer on X, saying: “SC Braga have sent an official bid worth €2m for Gustaf Lagerbielke to Celtic, negotiations ongoing.
“The player’s keen on the move.”
Lagerbielke has three years left on his contract but is not favoured by manager Brendan Rodgers.
The centre-back showed promise in some early games, but injuries halted his progress.
He was loaned to the Dutch club after falling down the pecking order.
If accepted, the transfer would end Lagerbielke’s two-year stay at Celtic Park.