A report in Germany has claimed that the European champions are interested in signing the 25-year-old as they look to bolster their goalkeeping options for next season.
Madrid have been heavily linked with Manchester United's David de Gea and Thibaut Courtois of Chelsea, but Leno has reportedly emerged as a more viable option as he is said to have a release clause in his Leverkusen contract of just €20million.
Leno admits that the rumours are flattering but stressed that he is focused on Leverkusen's push for the European spots this term.
"It honours you when you are linked with Real," Leno, who made his competitive Germany debut in the 4-1 win over Azerbaijan last week, told Kicker. "But I want to fully focus on Leverkusen."
The player's agent, Uli Ferber, has claimed that foreign clubs have been tracking his development over the last 12 months.
"There was interest [from clubs abroad] last year, and there is interest again this year," he told Kicker.
Leno has played in every one of Leverkusen's Bundesliga matches this season, keeping a clean sheet on four occasions.