Alvarez, 26, spent the summer angling for a move to LaLiga rivals Barcelona, a move that Atletico Madrid refused to sanction.
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The Argentina international has since returned to the fold under Diego Simeone, coming off the bench in two of their four league games so far.
Simeone brought him on for the final 31 minutes of the 3-0 defeat to Athletic Club, but with his side already 2-0 down, Alvarez had little impact.
Speaking to ESPN after the game, midfielder Llorente admitted that Atletico need the striker to get back to his best.
"He (Julian) is a very important player for us," Llorente said.
"He knows it. He'll come in little by little, and the sooner the better, because we need his goals. We have to support him so he's at 100% soon."