The Merseyside derby might be played at St Mary's Stadium if Goodison Park does not receive the required safety certificate, according to The Athletic.
Premier League clubs voted that games should only be played at neutral venues as a contingency, however there is a growing concern about the Merseyside derby.
Wembley, the Tottenham Hotspur Stadium, and the King Power Stadium have also been listed as possible venues if games need to be played elsewhere.
However, it is thought that it would be easier and safer for the two sides to fly to Southampton rather than make the journey to Leicester or London by train or road.
A safety advisory group is set to meet on Wednesday morning to make the decision over the licence, including representatives from the police, ambulance, and fire services, as well as supporters' groups.
But a decision on venue could be delayed until after Manchester City's game with Arsenal, with Liverpool unable to win the title if Pep Guardiola's side beat the Gunners, therefore lowering the concern that supporters would turn up at Goodison.