The 31-year-old defender joined Everton in a £12 million deal this week after spending eight years at Swansea City, where he previously played alongside Davies in defence.
Williams, who skippered Wales to a semi-final spot at Euro 2016, is eligible to face Tottenham when the Toffees host their North London counterparts in Saturday's Premier League curtain raiser at Goodison Park.
But Everton boss Ronald Koeman told a press conference on Thursday that his latest recruit is unlikey to face Spurs, having barely trained with the Swans these past couple of weeks since the speculation started.
Nevertheless, Davies expects to meet up with the big defender behind the scenes and says he and his Tottenham colleagues are excited to test themselves against the Merseysiders in Koeman's first competitive game as manager.
"It will be the first time that I’ve seen him since those good times that we had after the tournament so it will be good to catch up with him," he told Tottenham's website.
"I think it’s a nice move for him, going there. He’s a top player, he’s shown that in the years he’s been playing for Swansea and Wales and from when I’ve played with him I’ve got nothing but good things to say about him.
"When I was coming through the ranks at Swansea it was nice to have somebody like him next to me who’s got that experience and leadership about him.
"He’s 31 now and he’s probably got the aim where he wants to go as far as he can and I think Everton is a good club for him. He’s going to be a good asset for them.”
“They’re going to be a good, well-organised side, especially with their new manager who they’re going to be out to impress so it’s going to be a hard game but it’s one that we’ll be ready for," the Tottenham left-back added about the match.
"Any game away from home in this league is tough, especially with the quality that the league has got so it’s going to be hard but it’s one we’re excited for and we’re going to be ready for it. Hopefully we can get a better result than last time at Goodison.”