The Brazilians have both long been on the Tottenham wishlist, and the club are set to try and move for one in January.
“We got in touch with Willian [in the summer] and he is one of the players that interests us,” Villas-Boas said in the Daily Mirror.
“I like his style, but we could not reach the value Shakhtar were asking. It does not mean we won’t try again.
“Shakhtar are a difficult club to negotiate with as they do not need the money and can keep their players.
“For Damiao, he had a spectacular Olympics. We follow the best players and youngsters. Leandro fits this profile.
“He has had injuries after London 2012, but he is a player that is always on our list.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.