The Argentine international joined Villarreal in January after the club paid £5 million, half the player's transfer fee, in order to bring him to Spain from Boca.
The 27-year-old has had an indifferent start to life in La Liga, but Llaneza travelled to Buenos Aires to thrash out the deal and he returned with positive news.
"The deal is nearly complete," he enthused. "Only the signatures are missing, but I doubt we will have any problems.
"It was a difficult situation for us all, but we have done what we set out to do and the player is now 100 percent Villarreal."
Boca drove a hard bargain, though, as Llaneza admitted that Villarreal have agreed to pay a further 1500 million pesetas in order to close the deal, 500 million more than their initial offer.
