The Toffees have struggled this season, winning just two of their eight Premier League games and are on the brink of dropping out of the Europa League.
On Thursday night, Williams showed his aggression in a negative way after getting caught up in a mass brawl during the second half of the Toffees' 2-1 defeat to Lyon.
Now, though, the former Swansea City centre-back has turned his attention to Arsenal.
"We all like him and I know myself we really want to try for him because when it gets like this the manager is the one who puts his head out there," The Express quotes Williams as saying.
"He is under pressure as we all are as players, and we want to deliver good performances and results. Sometimes you try that little bit extra for him and for everyone.
"So long as we fight [against Arsenal] that is the minimum we have to do at the minute. We have been showing fight and especially you can see the response from the crowd.
"That is the kind of thing we have to show them, show ourselves and show everyone really. That is the base line. The fight is the base and if you play well after that perfect."
The Merseyside outfit are just two points above the relegation zone.