Both picked up knocks in Saturday’s 2-2 home draw with Liverpool; Rodriguez in an early tackle with Virgil van Dijk, and Coleman who pulled up shortly afterwards and was substituted during the first half.
And Ancelotti revealed neither will have recovered in time to take part in Sunday’s Premier League match at St Mary’s Stadium, telling evertontv:
“Unfortunately, James had a problem during the game [against Liverpool]. 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.
“We are working this week on this and I think we are going to choose a good line-up for the game against Southampton.”
Coleman, he added, will miss “two or three weeks” with “not a big problem”.
Rodriguez and Coleman are the latest of a growing list of Everton absentees for the Southampton game, with Richarlison serving the first of a three-match ban following his red card in the derby.
Meanwhile, Mason Holgate (toe), Jarrad Branthwaite (ankle), Cenk Tosun (anterior cruciate ligament) and Jean-Philippe Gbamin (Achilles tendon) remain sidelined by longer-term injuries.
But Ancelotti had brighter news on Jonjoe Kenny, who could return from an ankle problem he suffered in September’s win over West Ham in time to face Southampton.
The Italian was also coy on who may take the places of Richarlison and Rodriguez on the wings, saying:
“Alex [Iwobi] is a player who works hard. He is fast and with his quality he can help the team be better in certain situations.
“He 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.”