The pass master will turn 35 at the end of next season and Juve don't want to be caught short in that area.
Alonso was tracked by Chelsea and Liverpool in the summer window, but Luka Modric's metatarsal injury put paid to any hopes of a move.
A report in Italian paper Tutosport indicates that talks between Alonso and Florentino Perez began some time ago but never really took off.
It is thought that Alonso would complement the Bianconeri's style of the play with Antonio Conte a fan.
Alonso joined Los Blancos in 2009 from Liverpool for £30m.
His contract expires in 2014.