Leighton Baines has been offered a 12-month extension at Everton but Ashley Williams will leave the club when his contract expires at the end of the month.
Left-back Baines could extend his stay at Goodison Park into a 13th season after manager Marco Silva moved to keep the experienced former England international.
Signed from Wigan Athletic in 2007, the long-serving defender lost his place to Lucas Digne in 2018-19 and made just five Premier League starts.
Reports indicate Baines will take up the offer and bring an end to speculation linking him to Rangers.
Centre-back Williams, however, will not be returning to the Toffees.
Everton (@Everton) March 24, 2019
The 34-year-old was sent on loan to Championship side Stoke City last season and follows fellow veteran Phil Jagielka out of the door.
"Everton wishes to thank all departing players for their contribution throughout their time at the club," the club said in a statement.
A number of additional personnel changes are expected at Goodison Park while the transfer window is open, as Silva aims to build on the significant progress made in 2019.
The Portuguese endured a difficult first few months in charge, but Everton's form picked up towards the end of the season and they ultimately earned an eighth-place Premier League finish.