The 21-year-old spent a season on loan with the Lions before spells with West Brom and QPR.
Simpson is back at the Emirates Stadium but reports have suggested manager Arsene Wenger is prepared to let him leave.
"He was here before and everybody knows we admire him and he knows this club and we are just keeping tracks on it," Ambler told Southwark News.
"Simpson is one of the players we are looking at. But quite frankly I don't expect us to move forward until next Thursday when everyone is back in training."