Khedira has been sidelined since tearing the anterior cruciate and medial collateral ligaments in his right knee during Germany's friendly against Italy in November.
The 26-year-old successfully underwent surgery to repair the damage and has been recovering in Augsburg, Madrid and now in southern Sicily.
It is not yet known when Khedira will be able to play competitively again, but he feels he is close to returning to squad training with his Real team-mates.
"I feel more like a footballer now, because being here, on a football field, is like being home again. I can sense that I'm reaching the end of it, I'm close to getting back to the team and that motivates me to keep fighting", he said on www.realmadrid.com.
"It was tough at the beginning. I think the first four or five weeks were the most difficult. I was on crutches and couldn't walk... I was very limited.
"In recent weeks I've been training more comfortably on my knee. I'm really happy to be back on the turf, with the ball and running around outside. I have more confidence in my knee now, and I also feel more secure. I'm well."
The former Stuttgart player, who moved to Spain in 2010, also hailed his Real colleagues for their support in his battle to get back to fitness.
He said: "I miss the team, my team-mates, the manager... It's tough training on your own every day. It's important for me to stay in touch with my team-mates and the boss, it makes everything easier.
"It's a pleasure having team-mates like them. They're great people with big hearts. We have the opportunity to win three titles. Especially in the Champions League, all the Madrid fans want us to win, and we want it more than anyone, for sure."