Williams told ESPN's Josina Anderson that he would like to visit with four to five teams before making a decision on where he will sign.
Williams' planned visit to Miami was first reported Saturday by the NFL Network.
Long one of the NFL's top pass-rushers, Williams had only five sacks last year for the Bills, who released him Tuesday.
Miami placed a $12.734 million transition tag on Vernon on Tuesday, allowing him to negotiate with other teams. The Dolphins have the right of first refusal to match any offer.
Wake, 34, is coming off a torn Achilles tendon, and the Dolphins have been negotiating to lower his $9.8 million salary cap hit.
Williams, 31, has 96 career sacks, but his production fell last year under new Bills coach Rex Ryan. At times, Williams complained about his role.
Williams, the first overall pick of the 2006 NFL draft by the Houston Texans, is a four-time Pro Bowl selection, earning trips with the Bills in 2013 and 2014. Over his first three seasons with the Bills, 2012 through 2014, Williams made 38 sacks -- the fourth-most in the NFL over that span.
ESPN Bills reporter Mike Rodak and The Associated Press contributed to this report.