The Blues completed the loan signing of Gonzalo Higuain last week, and the Argentine’s arrival is likely to further limit the World Cup winner's chances of regular first-team football at Stamford Bridge.
Giroud himself has said that the signing of Higuain would likely influence any decision over his future in England, and suggested that a return to France was an alternative he was considering.
And Aulas has now opened the door to a potential move to Lyon, but insists that it would have to be a deal done in the summer.
He told Le Figaro: "I dreamed of bringing him in last summer and I even called Arsene Wenger to get his opinion, someone like Gerard Houllier knows him well too.
"We had discussions when I was in Moscow with the French national team during the World Cup. Things were not possible, on his side.
"Today we have an attack that is well stocked. If someone in the front left, then a deal could interest us, especially because he has a different profile compared to our players."
He scored 105 goals in 253 games in all competitions for the Gunners before leaving for Stamford Bridge in January 2018.
A return to Ligue 1 would kindle memories of his last season in the French top-flight, when he led the line for Montpellier as they recorded a shock league title success in 2011-12.
"This summer, of course Giroud will interest me," reiterated Aulas. "It seems a little tight for this winter. We do not want to overload with attackers, especially as we have a real team.
"Aside from that, we will have to see what manager we have at that moment of the season, but I like this boy. He is a good guy."
Chelsea are next in action on Wednesday night when they face Bournemouth as they aim to move three points ahead of fifth-placed Arsenal following their win over Cardiff City.