During the summer, the former Chelsea star was allowed to depart Real Madrid a year before the end of his contract.
Hazard endured a disastrous four-year spell at the Bernabeu, only featuring on 76 occasions courtesy of a spate of injuries and falling out of favour with Carlo Ancelotti.
The 32-year-old featured for just 325 minutes across nine outings in La Liga and the Champions League during 2022-23, resulting in the Spanish giants cutting their losses.
With Hazard having already announced his retirement from the Belgium national team, there have been suggestions that the playmaker may soon hang up his boots.
That speculation has remained throughout the last few months with Hazard having not agreed terms with a new club, despite a number of potential clubs having been linked.
Nevertheless, according to AS, Union SG are prepared to offer a contract to the legendary figure.
Union SG have been one of the top clubs in Belgium in recent seasons, finishing runners-up in 2021-22 and third position during the most recent campaign.
They also reached the quarter-finals of last year's Europa League and are currently preparing to begin their group-stage campaign in the 2023-24 edition.
The report suggests that Union SG are hoping that Hazard will be attracted to the chance to play in Brussels at the same time as his two brothers.
Thorgan Hazard is plying his trade at Anderlecht, while Kylian Hazard is associated with recently-promoted RWD Molenbeek.
Whether that proves to be a factor in any decision remains to be seen with Hazard still living in Madrid, a city where he and his family are settled.
His free-agent status means that he can join a club that still has spaces remaining in their squads for the remainder of the calendar year.