Looking ahead, Ramos is scheduled to start Thursday night in Port Charlotte against the Twins; Odorizzi will also pitch in that game. Bedard will then start Friday against the Blue Jays at Charlotte Sports Park.
Rays manager Joe Maddon said a decision will probably be made "the next day after that," which is Saturday.
"We've got to make up our minds," Maddon said.
Bedard has an out in his contract if he does not make the Major League team, and he has made it clear that he would go elsewhere if he doesn't make the club due to the fact that there are many Major League clubs that need starting pitching.
Maddon understands Bedard's decision.
"We would not want to hold him back if he was not chosen," Maddon said. "I really like this guy a lot. He's really ingratiated himself to a lot of us in a very brief period of time. He's a professional. He's definitely still good. So it's just one of those things, where if in fact he wasn't a fit for us and he is for somebody else, you want him to take advantage of that opportunity."
Maddon said the possibility of losing the veteran left-hander would not influence the final decision. When asked if Bedard would be a bullpen candidate if he didn't win the fifth spot, Maddon said that given all the bullpen candidates the Rays have, "I think it would be hard to want to do that."
Coming into camp, the Rays knew they would have a stiff competition for the spot created by Jeremy Hellickson's right elbow surgery. The right-hander will be out until early June after having "loose bodies" removed.
"I don't think I could be happier with the way [the competition has] gone," pitching coach Jim Hickey said.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.