Holgate is a player Everton are looking to sell, but they would also entertain sending him away from Goodison Park on loan.
Southampton are holding talks to try to loan Holgate, however they do not have an agreement on the amount of his wages they would pick up during the spell.
Everton do want to make sure they have found a replacement for the defender before they sign off on his exit.
Toffees boss Sean Dyche is keen to make sure he is not left short at the back by letting Holgate depart the club.
Holgate was not in the matchday squad on Saturday when Everton kicked off their Premier League campaign with a 1-0 defeat at home against Fulham.
He has slipped out of favour, with Dyche preferring other options ahead of him.
Everton are set to strengthen soon by bringing in winger Jack Harrison from Leeds United on an initial loan.