Reports on Monday linked the Germany Under-21 international with a move to Santiago Bernabeu after a string of impressive performances for the Bundesliga club.
Manchester United keeper David de Gea has also been strongly linked with Real, as they look to begin the process of replacing club captain Iker Casillas.
Leno was also in strong form during Leverkusen's penalty shootout exit to Atletico in the UEFA Champions League but the 23-year-old maintains he is content at the BayArena.
"I feel comfortable in Leverkusen and know nothing of any interest from Real," he told Kicker.
"And I give no attention to the rumours."
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