The Toffees missed out on their objective of European qualification at the end of 2025/26, despite a solid first campaign at their new Hill Dickinson Stadium base, and Moyes wants to hit the ground running in preseason.
Club captain Seamus Coleman has already moved on after his contract expired and veteran midfielder Idrissa Gana Gueye is yet to agree an extension after his own deal expired at the end of June.
Both parties had agreed to wat until after the 2026 FIFA World Cup to resume talks over a one-year renewal, and with Senegal now eliminated, the 36-year-old has a decision to make.
Pervious updates have indicated Everton are ready to part ways with a player who has made over 200 Premier League appearances across two spells on Merseyside as Moyes ties up a deal for Middlesbrough star Hayden Hackney.
Gueye's previous deal included an automatic extension clause, but the Senegal international did not meet an appearances threshold, and Teamtalk.com claim his international teammate Pape Gueye could now be a replacement option.
The 27-year-old has caught the eye across two seasons at Villarreal with 10 goals in 75 games as a roaming box-to-box midfielder and he's now boldly paused his international career after the World Cup.
Villarreal will demand in the region of €40M if Everton formalise their interest, but Moyes has opposition from several other Premier League teams at this stage.