A spokesman for the Welsh club declined to “comment on speculation” about the 31-year-old central defender.
But former Toffees wing Nevin told BBC Wales: “What’s not to like about getting Ashley Williams?”
Nevin added: “He understands the game, he has real bravery and is a real leader as well.
“I don’t think many Evertonians, or any fans of many clubs, would say no to Ashley Williams.
“Everyone is looking for a dependable centre half and he’s one. I’ve heard £10m – that would be great business for Everton.”
Williams is half way through a four-year contract at Swansea.
The Wolverhampton-born defender has played more than 300 games for the Swans since joining for £300,000 from Stockport in March 2008.
He hasn’t taken part in any pre-season matches after being given an extended break after captaining Wales to the semi-final of Euro 2016.
Comments by manager Francesco Guidolin did little to quell rumours following Swansea’s 4-0 win over Wolves on Saturday, 30 July.
“Ashley is very important to us but I don’t know what the situation is,” he said.
Former Wales team-mate Danny Gabbidon, speaking on Radio Wales, said: “It doesn’t look good for Swansea fans, I think he’s probably going to be going.”
Williams was linked with Everton during the summer of 2015 when her was seen as possible replacement for England international John Stones who was a target for Chelsea and Manchester City – though stayed at Goodison Park.
With Stones again being linked with a move to the Etihad Stadium, new Everton manager Ronald Koeman could need a new central defender.
Ins and outs at Swansea
The reported interest in Williams comes at the same time as rumours West Ham are poised to make a £20m bid for Swansea’s Ghana international striker Andre Ayew.
Ayew was Swansea’s top scorer last season with 12 goals in 35 Premier League appearances.
The Liberty Stadium club have already seen three forwards depart this summer with Portuguese striker Eder joining Lille, Italian Alberto Paloschi going to Atalanta and Frenchman Bafetimbi Gomis signing for Marseille on loan.
Swansea have not yet brought-in a new striker during the summer transfer window.
Former Wales striker and BBC Wales pundit Iwan Roberts says he is worried about the transfer policy.
“If these rumours are true I would think Ashley’s head would be turned at 31 to go and play for a big club – but for £10m he’s irreplaceable,” he said.
“You could see Ashley leaving and there’s a big question mark over Ayew.
“I can’t see Swansea turning £20m down when they got him on a free transfer.
“There’s only two weeks to go – there’s a lot of work to be done at Swansea City and I am worried for them.”