The England number one was widely criticised for his reckless tackle on Virgil Van Dijk which has ruled the Liverpool defender out for several months with knee ligament damage.
Merseyside Police have looked into threats made on social against Pickford and Richarlison, who was sent off late on in Saturday’s Merseyside derby for a challenge on Thiago Alcantara, but Ancelotti has no doubts about his goalkeeper’s focus.
“I don’t take into consideration to take him out,” said Ancelotti, who on Thursday said everyone at the club was sorry for the tackle but felt the reaction to it was “too much”.
“He played well, he was focused on the game. I think he is going to play on Sunday.”
Ancelotti was asked if Pickford had apologised directly to the player.
“I know that he was in contact with (Jordan) Henderson, he tried to be in contact with him but I don’t know if he was able to be in contact with him,” he added.
Everton had their own injury problems after that match with playmaker James Rodriguez sustaining significant bruising in an early challenge with Van Dijk and – although he completed 90 minutes – he was unable to train this week.
Ancelotti initially thought the Colombia international’s participation this weekend at Southampton was unlikely but was boosted by his return to training on Friday.
“James is not definitely out,” said the Italian, who 24 hours earlier had effectively ruled out Rodriguez.
“He had a big haematoma and was not able to train until today. He is much better now and we have confidence that maybe he can play.
“Fortunately, I think his recovery was really good and he trained today – he had a partial training session.
“I hope he is going to train tomorrow and we will see if he is in condition to play on Sunday.”
Ancelotti also confirmed new signing Ben Godfrey would make his full debut with right-backs Seamus Coleman (hamstring) and Jonjoe Kenny (ankle) unavailable.