Andre Villas-Boas has denied reports Tottenham have bid for Willian, although he concedes he is a fan of the Anzhi Makhachkala forward.
Even though Tottenham have spent almost £60million on new signings this summer, Villas-Boas is still looking for new additions to his squad as he looks to secure Champions League qualification.
The Tottenham manager was interested in signing Willian when he was at Shakhtar Donetsk last season and the Portuguese was also linked with the Brazilian when he was in charge of Chelsea.
Anzhi owner Suleiman Kerimov is looking to sell most of the club's highly-paid stars in order to shrink their vast wage budget.
At a press conference to announce Tottenham's support for NHS campaign 'Get to know cancer', Villas-Boas was asked whether he had made a bid for the 25-year-old former Shakhtar player.
He replied: "No, no." When asked whether he admired the player, the Tottenham manager said: "Yes. This is a player who I have spoken about in the past, not very long ago.
"He is a player who I appreciate. He belongs to them and I respect them so I wouldn't like to extend myself too much."
Liverpool are also thought to be keen on Willian's signature.
Tottenham broke their transfer record twice to sign Paulinho and then Roberto Soldado, while Nacer Chadli and Etienne Capoue have also joined in the last few weeks.
Yet it was clear from Sunday's 1-0 win at Crystal Palace, which came courtesy of a Soldado penalty, that the team are far from the finished article.
Spurs are light in defence following the sale of Steven Caulker and Villas-Boas concedes there is a good chance of at least one more player arriving before the transfer window shuts on September 2.
"We haven't finished," the 35-year-old said.
"We have a very, very good squad. We have done most of our activity in the market, but we are looking further on that. There is a possibility (of new signings), yes."
Despite the host of new arrivals on show in south-east London yesterday, the one question Spurs fans want clearing up is whether Gareth Bale will be at White Hart Lane next season.
Real Madrid are willing to break the world transfer record to sign the 24-year-old Welshman, but talks appear to have reached an impasse recently.
Bale wants to leave for the Spanish capital, but when asked whether he thought the forward, who has been out with a foot injury, had played his last game for the north London club, Villas-Boas said: "No. Not at the moment.
"He is a player who has had a clearing session (a light training session) today. Hopefully if everything goes well, the player will be involved and I can give you further news about the player in the future."
Bale will not travel with Spurs to Georgia tomorrow ahead of the club's Europa League playoff with Dinamo Tbilisi.
"He is in our Europa League squad, but he is not available (for Thursday's game) because he is injured," Villas-Boas added.
Two local cancer survivors, Steve Browne and Laurel Johnson, joined Villas-Boas today to launch Tottenham's season-long partnership with the 'Get to know cancer' campaign.
Prior to Sunday's home game against Swansea, Tottenham players will wear t-shirts and badges promoting the initiative, which aims to improve awareness and early detection rates.
Villas-Boas knows how dangerous cancer can be having seen a member of his close family, and his former mentor Sir Bobby Robson, fight the disease.
"A great example, alongside these two people here today, is Sir Bobby," the Spurs boss said.
"For all of the trophies that he won, the most important one was the way he fought cancer three times and for me he never lost the battle. He was always a great example of how committed and willing he was to fight it and he got the rewards out of it.
"This campaign is very strong and hopefully we can spread the word with projects like this."