The tragedy occurred when trouble broke out between supporters before kick-off at the stadium in Brussels. Liverpool fans were widely blamed and UEFA banned English clubs from European competition for five years as a result.
A Liverpool statement read: "Liverpool Football Club today (Tuesday) remembers the 39 football fans who died when a wall collapsed at the Heysel Stadium in Belgium on this day 27 years ago.
"Managing director Ian Ayre will lay the club's floral tribute at the foot of the Heysel Memorial Plaque in the Centenary Stand this morning.
"The tragedy unfolded on May 29, 1985, at the European Cup final between Liverpool and Juventus, when what should have been one of the greatest nights in the club's history turned into a nightmare.
"Instead of leaving Brussels having seen our team lift a fifth European Cup, Liverpool supporters travelled back to England having witnessed the deaths of 39 football supporters including 32 Italian fans of Juventus, four Belgians, two from France and one man from Northern Ireland."