Rooney has been in the centre of a media storm following continued revelations about his private life and claims that he met a prostitute while his wife Coleen was pregnant.
United manager Sir Alex Ferguson, who has included Rooney in his match-day squad, refused to discuss the striker's off-field problems at his press conference on Friday and said: "Let's put it to bed straightaway. I am not discussing any of my players' personal lives.''
Rooney, 24, played for England in Basel, Switzerland, on Tuesday and scored in the 3-1 victory, but there are concerns the level of abuse at Goodison Park, where Rooney is already a hate-figure after he quit the club to join United in 2004, could prove too much for the striker.
A Manchester United insider told The Sun: "Everyone has assumed Wayne will play because of how bravely he performed in Basel.
"But playing hundreds of miles away in Switzerland is a lot different to stepping out at Goodison Park, where there will be a lot of hatred and abuse flying around - all of it directed at Wayne.
"How can anyone give their best for 90 minutes in front of a baying crowd with all that turmoil going on in their private life?"
Meanwhile, defender Rio Ferdinand has declared himself fit for the Premier League clash with Everton after recovering from the knee injury that ruled him out of the World Cup.