The Mexican is reportedly unsettled at White Hart Lane, citing a lack of starting opportunities for his unhappiness.
"The negotiations are well on the way and it seems like the player wants to come to Villarreal," said the Spanish club's vice president Jose Manuel Llaneza.
"The deal is not finalised, but we expect a solution by the weekend. Villarreal needs more attacking players."
Dos Santos, 22, joined Spurs in 2008 from Barcelona.