Cape Town - Ashley
Williams wants Ronald Koeman to put the thought of taking over at
Barcelona out of his mind and focus on his job with Everton.
The former Ajax, Benfica, Feyenoord and Southampton manager, joined the club at the beginning of the season having taken over from Roberto Martinez.
While they finished their last campaign in 11th-place, this term the Toffees are on course for European football, in seventh place, just five points short of Manchester United in sixth, and qualification for the Europa League third qualifying round.
With Barca boss Luis Enrique having revealed his decision to step down from his job at the end of the current La Liga campaign, Koeman, along with number of well-respected managers have been link to the post.
But Williams, who was signed by Koeman, hopes to see the experienced manager remain at the club.
He said: "For me personally and the lads, we obviously hope he stays.
"He's started building a team here and we're all confident the future looks good for Everton so from our point of view we'd obviously want him to stay.
"But he might have his own ambitions. I can't speak for what he wants from his managerial career but just from our point of view, definitely we enjoy working with him.
"You can see form the way we've been playing of late that it's working.
"I think we're building a team, the gaffer is building a team to what he wants.
Everton lost 3-2 to Tottenham on Sunday, and Williams wants to see the kind of improvement at Goodison Park that has been evident at Spurs over the past couple of seasons under boss Mauricio Pochettino.
He added: "They're [Tottenham] a bit more settled than us, they play the same 11 most games and they know each other very well so that's where we're trying to get to.
"We saw it as a good test to see where we are as a team because they're clearly one of the best teams in the league.
"The gaffer is trying to build a team he wants and we've done well in the last couple of months. It's about kicking on now and trying to take that into next season."
Everton next host West Bromwich Albion at Goodison Park in an English Premiership clash on Saturday with Koeman's men in 7th position in the standings, five points behind Manchester United.
Kick off is at 17:00.