Talks with Gueye are said to be progressing well, while Coleman has been offered a new deal, with manager David Moyes particularly keen to retain the club captain in a playing role.
The Toffees entered the summer with over a dozen first-team players approaching the end of their contracts.
Most of those situations have now been resolved, though negotiations continue with Dominic Calvert-Lewin and Michael Keane over potential extensions.
Several long-serving and senior figures are confirmed to be leaving. Mason Holgate will depart at the end of the month, along with Joao Virginia, Abdoulaye Doucoure, Asmir Begovic, and Ashley Young.
Neal Maupay, meanwhile, will remain at Marseille permanently after his loan deal was confirmed to include an obligation to buy.
On the loan front, Armando Broja, Jesper Lindstrom, Orel Mangala, and Jack Harrison have all returned to their parent clubs following the conclusion of their temporary spells at Goodison Park.
However, Everton have secured the first signing of the window by turning Carlos Alcaraz's loan into a permanent deal.
Giorgi Mamardashvili has reassured supporters he was "fine" after being forced off during Merseyside derby action on Sunday, as Liverpool FC secured a 2-1 victory over Everton FC.
Arne Slot has praised his Liverpool side's mentality and character after a dramatic 2-1 victory over Everton in a tense Merseyside derby decided deep into stoppage time on Sunday.
Liverpool need a very late Virgil van Dijk goal to claim a 2-1 victory over Everton in their Premier League clash at the Hill Dickinson Stadium on Sunday.
Arne Slot has insisted the Merseyside derby remains "a very special game" as Liverpool prepare to face Everton in their latest Premier League meeting.
