According to Belgium-based journalist Dave Peters on Twitter, the centre-back on the second-tier side’s radar.
Burgess is out of contract at Pompey at the end of the season, with chief executive Mark Catlin conceding the popular defender's future is out of the club's hands.
Both parties have yet to come to an agreement on Burgess' future, despite opening talks on a new deal in January.
And it’s said that Union Saint-Gilloise could be the destination Burgess is heading for.
Writing on Twitter*, Peters said: ‘Union remains active in the transfer market. Now central defender Christian Burgess also comes from third division Portsmouth. Do signatures of Morris, Lapoussin and Perbet follow? #proximusleague #union #sources.’
Union Saint-Gilloise finished fourth in Belgium’s second tier last term and will be aiming for promotion in the 2020-21 season.
Les Unionistes are owned by Tony Bloom, who is also chairman of Premier League outfit Brighton. Meanwhile, ex-Genk boss Felice Mazzu was recently appointed manager to help the club achieve their aim of reaching the top flight.
Burgess joined Pompey from Peterborough in the summer of 2015.
The former Middlesbrough man has made 208 appearances and scored 12 goals at Fratton Park. On the way, he’s helped the Blues capture the League Two title in 2017 and the Checkatrade Trophy last term.
Burgess has been in his best form during his five years at the club throughout this campaign’s League One promotion push.
He’s also in the heart of the community during the coronavirus pandemic, volunteering his time to help residents who are most vulnerable.
Pompey have insisted they have repeatedly made it clear they wish to keep the 28-year-old, although Catlin has admitted nothing more can be done to convince him to remain.
* Peters’ tweet was translated via Google Translate.