Fabrizio Romano and Voetbal International's Tim van Duijn reported the rumour hours after Ajax won the Klassieker derby against Feyenoord (2-1).
Ajax were on the hunt for a new right-back after Devyne Rensch left the club in January for AS Roma in a reported €5 million deal.
According to Van Duijn, Ajax have agreed on a transfer fee of €2 million for the Brazilian defender who can play on both the left and right side of the defense.
Lucas Rosa has appeared in 21 games for last-placed Real Valladolid this season and provided one assist in the process. 24-year-old Rosa joined Juventus' youth academy in 2018 after leaving Brazilian side Palmeiras and moved to Real Valladolid in 2021 on a free transfer.
Ajax were targeting Rosa's team-mate Raul Moro earlier this transfer window but saw a deal for the 22-year-old winger fall through after the Spaniard suffered a lengthy shoulder injury.