As a former skipper of the Basque side, the defensive midfielder is in awe of his old team-mate, who is to lead the club for the last time against Valencia on Sunday
The Spain international played alongside the 33-year-old for nearly five full seasons before departing for Liverpool in 2004 and he has nothing but admiration for one of the Basque club's greatest ever servants.
"I have not seen a player more generous than Mikel," Alonso told diariovasco.com. "He always puts the collective before his personal interests.
"Mikel could have continued for one or two years more because he has always been in good physical condition and has so much quality.
"Even this season he seemed likely to play less because of the youngsters pushing hard for a place in the team, but eventually he returned to be one of Real's star players.
"But Mikel and I know what is required to play at the highest level. He has served Real for 14 seasons and wants to leave on a high."
Having captained Sociedad himself, Alonso is in awe of the way in which Aranburu has handled the intense pressure which comes with leading one's local side.
"It is clear that high-level football is very demanding psychologically, and especially if you play for your hometown team," the World Cup winner mused. "So this attaches even greater merit to what he has accomplished.
"With your hometown team you are never disconnected from the club because your family, your friends and the whole town live for the team."
Aranburu will skipper Sociedad for one final time in Sunday's Liga clash with Valencia at the Anoeta.