"For me personally and the lads, we obviously hope he stays," Williams told British media.
"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."
Koeman who joined the Merseyside club from Southampton at the start of the season and his side are on course to finish in the top seven of the Premier League for the first time in three years.
"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," the 32-year-old Williams added.
The Toffees, five points behind sixth-placed Manchester United, host eighth-placed West Bromwich Albion on Saturday and relegation-threatened Hull City on Mar. 18.
(Reporting by Hardik Vyas in Bengaluru)
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