Orlandi suffered the injury at the start of February, but was back in training on Tuesday and hopes to be involved when the Swans' second string face Fulham next Tuesday.
The injury came at a frustrating time for the 27-year-old Spaniard, who has found first-team opportunities limited this season, after he had impressed in the win at Aston Villa and the FA Cup third-round victory at Barnsley. And he is eager to start getting some game time under his belt.
He told the club's official website: "It was great to be back in training again. I wasn't at full pace, but just to be involved again was pleasing.
"Even training is very exciting here. The way the sessions are set up, and the energy the boys put in every single day ensures that it is very enjoyable. I have to take my time with this - the rehab has gone very well thanks to the physio team here.
"The next stage after a few training sessions is to test it in a match situation so I am hoping to play in the reserve game with Fulham. I will see how it goes every day in training until then and make a decision, but to play in that would be a big step."