The 29-year-old is reportedly set to complete a move to the Riverside within days.
Barragan has been a first team regular at Valencia for the last five years
The 29-year-old has been regular fixture at the Mestalla since his arrival in 2011, making a total of 110 appearances, netting one goal.
Middlesbrough manager Karanka is keen to strengthen his squad this summer
And after sealing deals for Victor Valdes, Viktor Fischer, Bernardo Espinosa, Marten de Roon and Jordan McGhee, Boro head coach Aitor Karanka is now poised to complete his sixth summer signing, as his side look to strengthen ahead of their first Premier League season in eight years.
Meanwhile, Karanka is also understood to be keen on bringing Barragan's club teammate Alvaro Negredo back to the Premier League.
Negredo endured a difficult time during his previous spell in the Premier League
Early indications show that the forward, who endured a disappointing spell at Manchester City before moving to Valencia, could be the subject of a loan bid from the Riverside outfit.
Middlesbrough celebrate with the trophy after being promoted to the Premier League
The Press Association also claims the club is looking to seal deals for Borussia Dortmund defender Neven Subotic and Uruguayan midfielder Gaston Ramirez, the latter of which spent the second half last season at the club on loan.