Spanish sources recently claimed that coach Jose Mourinho is monitoring the 26-year-old, who moved to the Premier League from Valencia in the summer of 2010.
However, Silva, who won Euro 2012 with Spain this summer, has declined to reveal whether there has been an approach from Los Merengues.
"I have just started my holiday and I am only thinking about resting," he told Canarias Radio.
|100/1||David Silva is 100/1 to win the 2012 Ballon d'Or with Paddy Power|
Silva started each of Spain's six matches in Poland and Ukraine, grabbing two goals and three assists as La Roja won the tournament, and he admitted to being delighted with his central role in the victory.
"When you have more playing time and you can help, you feel important to the team," he noted.
"The best moment? We were together for a month and a half with moments in which you are happier, and others in which you are sadder.
"I cannot just mention one moment in particular."