The pair, who both feature for Brazil at international level, were linked with Spurs during the summer and Portuguese boss Villas-Boas has reaffirmed his admiration for the duo.
Discussing Shakhtar's playmaker with Lancenet, he said: "We contacted Willian and he is one of the players in which we had an interest. I like his style but we could not reach a deal with Shakhtar in the summer.
|WE COULD HAVE WON - MCDERMOTT
|7/2||Reading are 7/2 with bet365 to survive relegation from the Premier League this season
"Shakhtar are a tough club to negotiate with; they don't need the money, they can keep their players."
Villas-Boas also had high praise for Damiao, who was one of the key players in the Brazilian team that won a silver medal at the 2012 Olympics.
He added: "There are many good players here, we are happy, but we obviously follow the best players and youngsters and Leandro Damiao fits in the profile.
"Leandro was spectacular at the Olympics but there are other interesting players. We are paying attention to his progress but he had injuries after the Olympics and may not have played that often.
"If he is within our reach, he'll always be in our list."