Barcelona, through the well-connected Ariedo Braida, have made contact with the Penarol midfielder's agent to register their interest. Despite their transfer ban this summer, as Braida's offsider Charly Rexach asserts, "We can still register players and bring them here in 2016".
Which would suit both Barca and Penarol, where coach Pablo Bengoechea has declared he expects to introduce 16 year-old Valverde to senior football next season. The free-scoring midfielder led Penarol to the U16 title last year, thumping River Plate in the final, and is ready for the next step.
Wenger is aware of Barca's sudden interest and is unlikely to step aside.
While Valverde's impressive U17 South American Championships brought the Uruguayan to the world's notice, tribalfootball.com can reveal it was another tournament, last October, which first had Arsenal scouts alerting Wenger to his talent.
Late, last year, in preparation for the South American Championship, Uruguay toured France, competing in the Lafarge International Tournament. Valverde was a standout, as Uruguay finished tournament winners.
Such were the reports delivered by his scouts, Wenger immediately invited to Valverde to trial at London Colney, only for Penarol to turn it down.
But the Gunners boss was insistent and had club representatives continue to badger the Uruguayans through to Christmas until Penarol's board relented.
Rodolfo Catino, the Penarol president, said on the eve of Valverde flying to London in January: "Penarol has no intention of selling him to Arsenal or any other team. However, this club was so insistent that we agreed he could travel to England and spend a week there."
Such was Wenger's eagerness to take a closer look at Valverde, he also agreed to a €4 million insurance penalty should the youngster be injured while in Arsenal's care.
During that week in January, Valverde, still only 16, began with the U21s, but was soon promoted to Wenger's senior squad and closed out his trials training alongside the likes of Alexis Sanchez and Mesut Ozil.
By his own admission, Valverde loved the experience, "...it was tremendous, training with professionals and learning new things" and London also rubbed off on the youngster, as he returned home with a new mobile skinned with a Union Jack!
But Arsenal must move quickly, as five goals in February's South American Championship has led to Barca getting in touch.
The Gunners aren't standing aside, with talk of a £2.5 million fee emerging. Early negotiations include bonuses to be added based on Valverde's progress through the ranks at London Colney.
For their part, Penarol see Valverde as an addition to Bengoechea's first team next season.
"It's in my mind to promote him. He does things other players, much older, only do. He plays as a man, as a professional," enthused the coach.
"I see his promotion as a natural step. Myself and the board agree. I see him fully engaged in the first team next season."
As Bengoechea insists, Arsenal and Barca will be battling for something exceptional.
He added: "I think the players under 20 have the physical conditions to play in the First Division. For the boys under 17, they still need to grow a little more, they are still children.
"But there's always been exceptions..."