Simeone, who won the Liga and Copa del Rey double with Atletico as a player in 1996, said: "(Pellegrino) is working with a lot of enthusiasm.
"He is a very intelligent lad and with the team he has in Valencia for sure he's going to have a great season, I have no doubt about that."
Atletico have been in superb form under the inspirational Simeone, but face a stiff test on Saturday at 11th-placed Valencia, who are looking to get their season back on track after an erratic start.
Unbeaten Atletico lie second in La Liga with 25 points from nine matches, behind Barcelona only on goal difference.
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