The Wales international has been the first-choice left-back at the Liberty Stadium for the past two seasons and is reportedly a target for new Tottenham head coach Mauricio Pochettino.
But Williams, who signed a new four-year contract at the club last week, says he will talk to Davies about his future shortly.
"It is down to Ben what he wants to do," Williams is quoted as saying by the South Wales Evening Post. "I have not had the chance to chat with him, but obviously I am close to Ben, we have played a lot together and get on well. I have seen him grow, we know he is a mature, sensible lad and he will do what is best for him.
"I will try to advise him, but I would not tell him to stay because I want him to stay.
"That might not be best for him. I don't know what he is thinking, I would like to have that conversation with him.
"Obviously we want our best players and I would be over the moon if he were to decide to stay. If he feels he needs to go and the club think it is right then that is how it will go.
"Tottenham are a big club, they are not a small team, and if he wants that then brilliant, and I would back him all the way."
Swansea have the luxury of having two perfectly capable left-backs at their disposal, and Neil Taylor - the man whose ankle injury at the beginning of the 2012-13 campaign opened the door for Davies to make his first-team debut - would be a ready-made replacement.
And Williams, who captains Davies at both club and international level, concedes his defensive colleague would fit in well at White Hart Lane.
"He would fit in well there without doubt," added Williams. "If he does not go now and we don't make it to the top then he will leave at some point because he deserves to be at the top of the league.
"We will see how it pans out."
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1
Get FourFourTwo Newsletter
The best features, fun and footballing quizzes, straight to your inbox every week.