"I can't believe that we have an interest in either," Ryan told 103.3 FM's Galloway and Company.
"I don't see that's an upgrade" to the Rangers' bullpen, Ryan said. "And Beltran, you worry about his knee. And you're taking on an awful lot of salary."
Ryan said that the Rangers have started trade discussions with other clubs, with interest picking up as the division races take shape.
Beltran, who is making over $19 million in 2011, is batting .278 with 10 home runs and 49 RBIs. He is also eighth in the National League in drawing walks (40). But he has a history of injuries with the Mets and missed the first half of last season after surgery on his right knee.
"He's had so many medical problems and played so little at times, it's just a real risky situation," Ryan said.
Rodriguez, who is making just over $12 million this season, has 20 saves and 41 strikeouts in 27 innings. The closer said last week that he would give up his closer's role if he were traded to a contender.
The non-waiver trade deadline is July 31.
"The only thing I thought about that is, I guess there weren't any blue-eyed players prior to lights," Ryan joked.
Rangers manager Ron Washington rested Hamilton on Sunday, a day after the reigning American League MVP went 0-for-4 with four strikeouts using tinted contact lenses. He saw 17 pitches in the game -- 15 of which were strikes.
"His history is he hasn't performed well in day games," Ryan said. "We don't have an explanation as to why that is. Hopefully he'll find something that will help him, and then if Ron's going to rest him, I would venture to say that the day games are a good day to rest him as he did (Sunday).