The Brazilian feels the striker is on a par with the Manchester City man after he guided Atleti to victory over Espanyol at the weekend
Filipe Luis played alongside the Argentine in 2010-11 before the latter left for Manchester City and the left-back feels Costa believes the match-winning qualities of the pair are striking similar.
"Each time we are struggling a bit, Diego Costa steps up and makes the difference," the Brazilian defender told AS.
"He really reminds me of Kun Aguero when he was at his best for Atleti. Sometimes things got complicated and then Kun created something from out of nowhere.
"Diego has that quality as well. When the going gets tough, he's able to do something special as well.
"We can only hope that he keeps up this level. It's great to have him in our team. He has what it takes to become a true great."
The 25-year-old Costa has been in fine form for Atletico in 2013-14, scoring 22 goals in 27 La Liga games.