Alonso, 31, missed June's Confederations Cup to have surgery on a groin problem and then broke a bone in his foot in training in August.
"I hope to be back soon," Alonso said on Real's website (www.realmadrid.com).
"I am making progress and my come back is not far away but I don't want to talk about dates. There is no fixed date," added the former Liverpool player.
"People who have had this (groin) injury know that the recovery can be treacherous.
"We don't want to rush things. It is a complicated injury that I would not wish on anyone."
A consummate passer, Alonso has been a key performer for Real in his central midfield role since joining in 2009 and they have struggled to exert the same level of control over opponents in his absence.
Without him, coach Carlo Ancelotti has had to rely on Croatia international Luka Modric, Germany's Sami Khedira and new signing Asier Illarramendi and Real's La Liga campaign has got off to a stuttering start.
"I am still in the phase before joining the main group (in training)," Alonso said.
"Then I have to get up to match pace because the competition has started and it is more complicated having not played at all.
"There are some injuries that you know the recovery time for. The foot does not bother me too much but the groin injury is more treacherous."
Real, five points behind joint La Liga leaders Barcelona and Atletico Madrid after eight matches, host Malaga on Saturday before Italian champions Juventus visit in the Champions League next Wednesday.