Ramirez, a three-time All-Star and a career .306 hitter in six full seasons, would have to change position because of the Marlins' free-agent addition of Jose Reyes, who agreed to a six-year, $106 million contract Sunday.
"Hanley doesn't want to play third base and the Marlins were informed of that," the source said. "Rather than ask for a trade, what he has done is to inform (the team) that he does not want to play another position other than shortstop."
Meanwhile, Andy Mota, Ramirez's agent, told ESPNDeportesLosAngeles.com he had no comment.
The only public comment that Ramirez has made since Reyes' deal came to fruition was through his Twitter account.
He wrote Tuesday: "What I can do now is work hard and be prepared for next season because that's all that I can control, I love you all !!!!"
Ramirez is under contract with Miami for the next three seasons. The Marlins owe Ramirez $47 million until 2014, thanks to a six-year, $70 million extension he signed in May 2008.
New Marlins manager Ozzie Guillen said he would understand if Ramirez feels neglected because of Reyes' deal. He spoke with Ramirez before the agreement with Reyes came to light and plans to call him soon to talk more about it.
"He must understand what is best for the club and he will be a better player having those two guys in front of him in the lineup," Guillen said at the winter meetings about Reyes and Emilio Bonifacio.
"The last thing we would do is slap the guy and say, 'you have to move.' That is not the way," Guillen said. "I think the boy will have the opportunity to be an All-Star third baseman. We have the opportunity to have two All-Stars in these positions, " Guillen said.
Enrique Rojas covers Major League Baseball for ESPNdeportesLosAngeles.com.