Alonso is yet to play this season after undergoing groin surgery in the summer.
The 31-year-old decided to go under the knife, rather than compete in the Confederations Cup, only for his return to be delayed by a broken foot suffered in training.
Reports in Spain have suggested that Alonso could be back in time for this month's El Clasico against Barcelona, but Alonso has downplayed such suggestions.
Instead he is focusing on continuing his slow, but steady, recovery from a "tricky" injury.
"I hope to return soon. It has been a difficult summer," he told reporters at a function on Tuesday.
"I then had to push back my recovery after breaking my foot in training, but it is now getting closer.
"I need to respect what my body is telling me and not put the stress of a deadline on my return.
"At the moment I am training by myself and I'm at a point where I am close to returning to the main group.
"I still need to do a few things before I can fully join them.
"This is a tricky injury and I have to take it day by day. I am close but I have a way to go yet.
"I speak to the doctors a lot and it is important I don't rush anything or risk taking a backward step.
"This is a complicated injury. Some injuries you know a deadline but not this one. But now I have a good feeling."