The Swansea City defender is expected to complete a £10 million move to Goodison Park.
The Blues have been in search of a defender all summer after their defence struggled under Roberto Martinez once again last season.
They are also looking to plan ahead should John Stones end up completing a big money move to Manchester City.
Several names had been linked with a potential move, but it appears they have set their sights on Wales international Williams.
The Swansea City defender is expected to complete a move to Goodison Park before the end of the week after the Blues agreed a £10 million fee for his services.
The clubs fans have largely welcomed the news, and Nevin says it represents great business at the reported fee.
“What is not to like about getting Ashley Williams?” he told BBC Sport.
“He understands the game, he has real bravery and is a real leader as well. Everyone is looking for a dependable centre half and he’s one. I’ve heard £10m – that would be great business for Everton.”
Should Williams complete the move as expected, it will be interesting to see if he is the only central defender to arrive at the club this summer.
The defence has been a particular weak spot for Everton for several years, but that was largely blamed on Martinez’s tactics rather than the quality of the players.
Koeman clearly believes additions are needed though, and it remains to be seen if he thinks Williams is enough to solve their issues.
Wales' Ashley Williams and teammates celebrate at full time