Rodriguez suffered an injury during a clash with Virgil van Dijk at the beginning of last weekend’s Merseyside derby draw with Liverpool.
Although the Colombia international completed the 2-2 encounter, Carlo Ancelotti has confirmed that he is unlikely to feature at St Mary’s on Sunday.
The Premier League leaders are also set to be without captain Seamus Coleman, who will be sidelined for three weeks with a minor injury.
“Unfortunately, James had a problem during the game [against Liverpool],” said Ancelotti.
“He had a mistimed tackle with Virgil van Dijk at the beginning of the game and I think he will not be available for the game against Southampton.”
Everton’s prospects on the South Coast had already been dealt a blow by Richarlison’s red card for a foul on Thiago Alcantara in the Goodison derby.
But Ancelotti believes the setbacks within his squad can provide a rare opportunity for players on the fringes like Alex Iwobi and Anthony Gordon.
He added: “We have to put in other players who have the desire to play.
“We are working this week on this and I think we are going to choose a good line-up for the game against Southampton.
“Alex is a player who works hard. He is fast and with his quality he can help the team be better in certain situations.
“He [potentially] has an opportunity to play but also we have Bernard and Anthony Gordon.
“We have a lot of opportunities to replace Richarlison and James.
“We are already moving on.”