Quarterback Trent Green is finally with the Miami Dolphins in South Florida, where Daunte Culpepper's time is running out. Green passed his physical with the Dolphins, completing a deal in which Miami acquired him from the Kansas City Chiefs for a fifth-round draft pick in 2008. Green's agent, Jim Steiner, said the Chiefs may get a fourth-rounder instead, depending on how Green fares in Miami this season. The team scheduled a news conference to announce the deal. It's expected that Green will be on the Dolphins' practice field June 8 when the team opens a three-day minicamp. "I think everybody knows what this defense has done here ... " Green said. "It's time for the offense to catch up." He'll immediately be penciled in as the starter in Miami, which went 6-10 last season and missed the playoffs for the fifth straight year. Like Green, Culpepper wants to be there for minicamp, too -- but that's hardly a sure thing. A few hours before the Green trade became official, the Dolphins told Culpepper they "are going in a different direction at the QB position," according to Culpepper, who is resisting that plan. "They would like to trade me in order to 'get something for me,"' Culpepper, who is his own agent, wrote in an e-mail after meeting with Miami general manager Randy Mueller and first-year coach Cam Cameron. "However, it is my position that I have already been down that road and I am not interested in being traded."