Liverpool are already in talks over a Premier League victory parade and have reportedly agreed a route with the city council due to road closures.
The report adds that Monday May 18 has been mooted as a possible date, but could be put back if Liverpool are still in the Champions League.
Liverpool will not receive the Premier League trophy until the penultimate game of the season – their final home game against Chelsea scheduled for May 9 – despite the potential for a landslide victory.
If both Liverpool and nearest rivals Manchester City continue winning then the Reds could wrap up the title on April 4, if they beat Pep Guardiola’s men at The Etihad.
The current record for earliest title triumph is April 14, when Manchester United won it way back in 2001.
Meanwhile, Liverpool legend John Aldridge has said that a move for RB Leipzig striker Timo Werner would be a “great option” for Jurgen Klopp’s side this summer.
Werner has been in outstanding form for his Bundesliga employers this term, having scored 20 goals and six assists while appearing in every league game this season.
Such form has helped his side to cement their place at the top of the German top flight and, overall, Werner’s tally for the season stands at 25 goals in 27 appearances.
Various reports have indicated that Liverpool are keen on a move for the 23-year-old either in January or the summer, with the likes of Chelsea and Manchester United also linked.
A move for Werner this summer could coincide with a number of Anfield exits, with Adam Lallana out of contract at the end of the season and Xherdan Shaqiri heavily credited with a move away.