The 22-year-old, a £25million arrival from Norwich, is having to fill in at right-back due to an injury to Seamus Coleman and Jonjoe Kenny not yet being fit.
Godfrey replaced Coleman in the 31st minute of last weekend’s Merseyside derby for his first appearance for his new club and coped well with the double threat of Sadio Mane and Andy Robertson.
“Ben played a good game,” Ancelotti said. “After the first 15 minutes of the first half, where he had difficulty, the second half was really better.
“Also, you have to consider he played against one of the best wingers in the world in Sadio Mane.
“It was not an easy game for him but he was good, in my opinion.
“We tried him as a right-back this week in some exercises. He has all the qualities to play at right-back.
“I have no doubts about this and he will play there on Sunday.”
Everton are likely to have been replaced at the top of the Premier League table before kick-off at St Mary’s.
But Ancelotti knows they will have to be at their best if they are to regain their place at the summit.
“It will be a tough game. Southampton is a team with a really clear identity,” he added.
“They try to play with high intensity without the ball. They are really compact and it is difficult to find space to play.
“We have to be smart and clever with the ball. If we are clever with the ball, we have a chance to win the game.
“To win against them you have to be 100 per cent. I would like to be at 100 per cent because our target is to win.”
Striker Dominic Calvert-Lewin is likely to play a significant role if Everton are to come away from the south coast with three points.
The newly-capped England international is the Premier League’s joint-top scorer alongside Tottenham’s Son Heung-Min with seven goals from five appearances.
“I was joking with him. I said, ‘What is the most important goal that you scored?’. He was thinking about what was the most important,” said Ancelotti.
“So I said, ‘Don’t think about it. The next one is the most important so be focused there, the most important goal will be the next one’.
“He’s doing really well, but for the fact that he has done so well, everyone expects a little bit more.
“That has to be his motivation. He has to be ready to show a little bit more.”