The Brazilian full-back played with Aguero for a season in 2010, and believes Costa - who has been heavily linked with a move to Chelsea - has a similar style to the Manchester City man.
“Each time we are struggling a bit, Diego Costa steps up and makes the difference,” Luis told Spanish newspaper 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 for 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 teaks to become a true great.”
The £30m-rated Spanish international forward has spearheaded Atletico’s remarkable title challenge in La Liga this season. He has 22 goals in 27 league matches for Diego Simeone’s side, who are going toe-to-toe with Barcelona and city rivals Real Madrid for the title.
Chelsea have been sniffing around Costa since the January transfer window, with Blues boss Jose Mourinho expected to strengthen his attacking options this summer.
He has complained about a lack of goals in his team on numerous occasions this season, with Samuel Eto’o, Fernando Torres and Demba Ba struggling to find the back of the net on a consistent basis.
Eden Hazard is currently the club’s top goalscorer this term.