The Toffees have triggered the midfielder’s £7.1million release clause and he has been discussing terms with them this week.
Gana’s clause expires at the end of the transfer window but only Everton have made an official bid.
Villa, relegated from the Premier League last season, want to keep him but Di Matteo is resigned to seeing the Senegal international leave after just one season at the club.
He said: “It’s public Everton have triggered his clause and he’s going to leave. There’s no news so far but the expectation is, once personal terms are agreed and a medical (is done), he’s going to go.
“There are other clubs interested, that’s right, but the only official bid so far has been from Everton.
“There’s not much I can do because he had a clause in his contract and that’s something I inherited and my hands are tied. We will be losing him.
“The fact he is leaving is basically down to the clause he has in his contract, otherwise there would be no chance.
“We’re not a club looking to sell, we don’t have to, we don’t need to.”
Gana joined Villa from Lille last summer and made 38 appearances, scoring once, as the club were relegated from the top flight last season – winning just three league games.
He could become Everton’s first major signing of the summer after they appointed former Leicester assistant manager Steve Walsh, who helped find Riyad Mahrez and N’Golo Kante, as director of football.