The Napoli and Uruguay striker has made no secret of the fact he wants to move this summer and he was also linked with Manchester City.
Napoli have since claimed City have pulled out of the race for Cavani because the Premier League club are not prepared to meet the 26-year-old's €63million (£54m) buyout clause.
That leaves Real and Chelsea to battle it out for the South American and he is flattered by the attention regarding his future.
He told media while at the Confederations Cup in Brazil: "Who would not be pleased by the interest of Real Madrid and Chelsea?"
But Cavani's immediate focus is on helping Uruguay to the semi-finals of the Confederations Cup ahead of their last group game against Tahiti.
The Copa America champions know they need to better the result of Nigeria against Spain in order to qualify having so far taken three points in the tournament.
Uruguay lost to Spain in their opening game but then beat Nigeria to give themselves a chance of qualifying and Cavani said: "I am concentrating only on the national team and the Confederations Cup.
"After the loss against Spain, we got what we needed against Nigeria to continue in the tournament."
He added: "Today, I am a Napoli player and I do not want to think about other things."