The 27 year-old Uruguay international admits he wants to return to Penarol before he retires.
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"I love Peñarol. I'd like to end my career by winning something important with the club and with Uruguay," said Valverde.
"I'd like to return in good physical condition, not to 'steal' money; in fact, I'd even go to Penarol for free."
Valverde also admitted a great admiration for Argentine giants River Plate.
He also told Terapia Picante: "I could never watch Peñarol, but I watched River every weekend. I grew up watching them; for me, Argentine football was the best."