However, Sky Sports understands a deal for Atletico Madrid's Pizzi looks unlikely to be finalised.
Pacos de Ferreira midfielder Vitor is expected to finalise his switch to Boro this week, having already held talks with the English outfit.
The 29-year-old attacking midfielder played 29 games of Pacos's outstanding campaign last season which saw them claim third place in Portugal's top-flight - thus gaining them a Champions League play-off spot for next season.
But Vitor looks unlikely to taste Europe's elite tournament as he will instead be lining up in the Championship with Boro.
Boro had hoped to bring in Vitor's compatriot Pizzi - who spent last season on loan at Deportivo La Coruna from Atletico, and he impressed with eight goals in La Liga.
The 23-year-old international forward was being lined up by Boro for a loan switch, but instead he looks set to sign for giants Benfica with local Lisbon media claiming a five-year deal is set to be finalised.
"Negotiations are well advanced with Benfica, but there is still no agreement. Though I think everything could soon end well," Atletico president Enrique Cerezo is quoted by Portuguese daily Abola.
Middlesbrough have also been linked with another Atletico player in the shape of young striker Borja Gonzalez - who spent last season on loan at Huesca.