An amber weather warning is currently in place for Storm Darragh, starting from 02:00 CET on Saturday until 07:00 CET on Sunday, with inland winds expected to reach 60mph to 70mph.
The Premier League fixture at Goodison Park gets underway at 13:30 CET on Saturday and both clubs have advised their supporters to take extra care around the ground.
Merseyside Police are advising against all "non-essential travel" and to "plan ahead", while the Met Office warn of potential power cuts and travel disruption with "flying debris and falling trees could result in a danger to life".
Both clubs have held meetings and it is being reported discussions over whether the match will take place continue in the morning.