Join The Club
Alonso made his first appearance of the season as a substitute in Wednesday's 7-3 triumph over Sevilla, following a five-month lay-off with groin and foot injuries, and could return to the starting line-up when Madrid face Rayo Vallecano on Saturday.
Illarramendi has deputised in the absence of the Spain international, but acknowledges Real are a better team with Alonso fit.
"He is important for us; he has been here for a long time and has always been important," said Illarramendi.
Article continues below"There will be more competition and that is good for the team and helps us all to improve. We have a match every three days and we will have to rotate to get rest.
"The important thing is carry on as we are whoever plays."
Only Granada have mustered a lower tally than Rayo's eight and Paco Jemez's side have also conceded 27, more than anyone in the division.
