The 36-year-old has said he is targeting one final challenge in club football before hanging up his boots, and the A-League side are monitoring the situation.
"He's certainly a player it's hard not to have a look at," coach Tony Popovic said, adding that the club was considering several new players.
"But obviously Robbie is the one everyone is talking about at the moment.
"He's had a fantastic career, he's a great player and still scoring goals, so he's certainly a player we'd have a look at."
The former Liverpool and Spurs star, who is Ireland's record goal-scorer with 68 from 146 appearances, was one of the most successful foreign players to ply his trade in the US top flight.
He helped Galaxy win three MLS Cup titles while scoring more than 100 goals in all competitions after signing for the club in 2011.
His departure announcement last week came shortly after former England and Liverpool captain Steven Gerrard said he was also leaving the club.