The 24-year-old, who arrived at Villa Park from Juventus last summer, scored once in 32 games on loan at Valencia across all competitions last term.
Barranechea impressed under former West Brom manager Carlos Corberan, as Valencia climbed from relegation trouble into the top half of La Liga.
He was also called up by world champions Argentina for the latest round of World Cup qualifiers, but was an unused substitute in a 1-0 defeat at Chile in June.
Portuguese publication Mais Futebol have claimed that Barrenechea has moved up on Benfica's list of potential targets, with the Portuguese heavyweights considering him as a replacement for Florentino.
The reports adds that Villa would be open to selling Barrenechea for the right price, with Valencia also monitoring his sutiation.
However, that is reportedly expected to be on another loan deal, which would only be possible if Villa choose not to sell this summer.
Barranechea had also attracted interest from Real Betis earlier in the window, but they opted against signing him due to finances.
Villa signed Barrenechea as part of a double transfer from Italian giants Juve, which saw Samuel Iling-Junior also head to the West Midlands for a fee of £6.91 million including £2.59 million in add-ons.
The deal was also related to the transfer of Douglas Luiz, who headed in the opposite direction, despite being a separate transaction.
Unai Emery's side have made just one signing so far this summer with the arrival of teenage Turkish defender Yasin Ozcan.
They begin pre-season preparations with a trip to local neighbours and League Two side Walsall at Bescot on Wednesday evening.