The Senegal international has been a key player for the Toffees since he joined for £7.2m from Aston Villa in August 2016.
And Everton caretaker boss David Unsworth confirmed the club are close to finalising a fresh deal for the 28-year-old.
“I believe we are very close which is fantastic news for Everton,” Unsworth said.
“We are very close and that’s great news for Idrissa and great news for me. He’s been great over the period of time. I have seen his performances.
“At Aston Villa he was a top player as well and a humble guy. So to tie him down for a number of years is great.”
Unsworth has no fresh injury concerns ahead of Everton’s trip to face Leicester on Sunday.
He also revealed midfielder Ross Barkley could return from a hamstring injury at some stage next month.
However, Yannick Bolasie (knee) and Seamus Coleman (broken leg) are still quite a way off.
“The long-term injuries are as they were. Ross is maybe three or four. Yannick and Seamus are months,” Unsworth said.
Unsworth also urged his players to leave the baggage behind from Ronald Koeman’s reign and start looking forward.
“What has gone before is gone,” he added. “This is a new chapter and a nice challenge. They have shown me there is a good team there.
“ I like a smile about the place and an atmosphere where players feel free to express themselves in a team environment where there is 100 percent effort.”