Galatasaray's director, Levent Nazifoglu, has confirmed the club's interest in the 29-year-old.
Leiva is currently playing for Liverpool. He joined the club in 2007 form the Brazilian club Gremio.
Nazifoglu told 'GSTV':
"One of the players we are interested in is Leiva, but there are other alternatives.
"One of them will be up front".