Williams also cited the arrival of new offensive coordinator Brian Daboll as an indicator of new things to come.
"We are not the same offense we were two years ago," Williams said. "I think new offensive coordinator. I think they might want to go in a different direction."
The 11-year NFL veteran was scheduled to become a free agent before the start of the NFL lockout last month, but he remains open to staying with the Dolphins, with whom he has been since 2002.
"If the Dolphins really want me to stay and make a fair offer, it would be hard for me to turn down, but I don't know if that is going to happen," Williams said.
"I have things to offer that a rookie can't offer," added Williams, who rumbled for 673 yards and two touchdowns in 16 games last season, averaging 4.2 yards per carry. "I think I bring positivity. I think I bring leadership. I've proven I can play at a high level consistently."
Brown, who started all 16 games in 2010 and rushed for 734 yards on 200 carries, also is without a contract.