The Galibier is arguably the Tour de France's best known single climb and last year the race celebrated the centenary of its first ascent there in 1911 with its first ever summit finish, won by Luxembourg-born Andy Schleck.
"It's a possibility in 2013 and a probability in the next three Giros," Acquarone, who replaced Angelo Zomegnan as race director last year, said.
Seeing the Tour finish on the Galibier in 2011 has given Acquarone extra motivation to follow in the French race's wheeltracks.
"We're smaller than the Tour, so we're more flexible. And if the Tour did it, then so can we," he said.
"We have three different routes for 2013 and we will make a definitive decision in the two weeks after this Giro finishes."
Unlike the 2011 Giro - widely criticised for being too tough - Acquarone said the 2012 race, which started with three days racing in Denmark, is more well-balanced between difficult and easier stages and has a more international feel overall.
"Some people said we needed a tougher route in 2011 than in 2010, but it was too much. We had to give the race more equilibrium," he said.
"I wanted a race where riders like (world champion Mark) Cavendish can come for bunch sprints or have some Classic-like, hilly stages riders can try and win."
With the race on its second rest day on Monday, there is still no clear stand-out favourite this year unlike in 2011.
"Sometimes fans love to have a single rider like (now banned) Alberto Contador in 2011 who dominates the event and gobbles up the stage wins. This year there are lots of possible outcomes."
Spain's Joaquim Rodriguez is the overall leader with six stages remaining.
Acquarone said he had received no complaints from riders despite four crashes in six bunch sprint stages. Rather than the route itself, he believes the accidents are due to rising all-round motivation to win the race.
"I wouldn't say there are dangerous finishes, but some are technical," he said.
"The finish at stage five to Fano was technical and we had no crash, stage three to Horsens (in Denmark) was not technical and we had the worst crash.
"What's changed is that even at the Giro, now, all the stages are becoming more important and all the riders want to win. It's good for the race, everybody wants to stay near the front.
"I would be very worried if it was very dangerous, but the riders say they are fine with it."
The Giro d'Italia finishes next Sunday. After Monday's rest-day, racing resumes on Tuesday with a flat stage from Limone sul Garda to Falzes.