Dredge shot 6-under-par 65 in Saturday's third round, and is 13-under 200 through 54 holes.
Marcel Siem (67) of Germany is second at 11-under 202.
England's Oliver Wilson (67) is third with a total of 9-under 204.
Defending champion Sergio Garcia (68) of Spain is fourth at 8-under 205.
"If I can shoot around four or five under I will still have a chance," said Garcia. "The most important thing for me is to see that I am playing well, to see my putting is getting better."
"I have got myself in position a lot over the last couple of years and haven't managed to win yet," Dredge said. "I just keep trying."
Four players are tied for fifth at 7-under 206, including second-round co-leader Andrew McLardy.
Swim Week Miami Beach 2014 [PHOTOS]