The light aircraft flew over Merseyside towing a simple banner, which read: 'Dare to dream – will to win YNWA' during the Reds' 3-2 win over Manchester City.
The scenes were reminiscent of those at Old Trafford, when United fans paid for a banner to be displayed urging under-fire manager David Moyes to either quit or be sacked, reports the Metro.
An uninspiring first season since taking over as manager from Sir Alex Ferguson has left many Red Devils supporters disillusioned with ex-Everton boss Moyes.
His side looks like missing out on Champions League football, and possibly Europe altogether, while Liverpool under Brendan Rodgers is in a dominant position at the top.
Liverpool's hard-fought victory over City puts them in pole position for a first-ever Premier League title, and their first league crown since winning the old Division One championship in 1990.