"When I was cut, it was not a big surprise," Galyon said. "But I am really surprised I've come back as soon as I did."
As for the punting situation, the Dolphins made a contract offer to Turk, who also has drawn the interest of Minnesota and the New York Jets.
Turk had rejected a one-year proposal from the Dolphins several weeks ago, and the new offer is believed to be for three years with a small signing bonus.
The Dolphins entertained Royals, who has spent time with the Bucs and Saints, earlier this week and are prepared to make him an offer if they can't re-sign Turk.
Either way, the Dolphins would like to have the situation resolved soon.
Elsewhere, the Dolphins had wide receiver/punt returner Karl Williams in for a visit. Williams has spent the past six seasons with the Bucs.
Finally, the Dolphins are expected to talk to veteran defensive ends Michael Sinclair and Rob Burnett after the draft after losing Lorenzo Bromell to the Minnesota Vikings.
Bromell reportedly has been told he would be a full-time starter at right defensive end in Minnesota, where he will be reunited with former Dolphins defensive end Kenny Mixon.