That doesn't mean the Astros are necessarily the favorites to sign Clemens either, though the two sides can open negotiations starting next Monday.
"[Clemens] does not intend to play in May, so the May 1 date does not mean much," Randy Hendricks, who along with brother Alan represents Clemens, told MLB.com via e-mail Monday.
Clemens spent Sunday night in a Houston hospital where his son Koby, an infielder in the Houston system, was undergoing surgery on his finger.
"He's going to miss about six weeks," Clemens said. "That's kind of my main concern right now. He's going to get through this week and we'll get him back out there and that's kind of what I'm focused on right now."
Clemens said he has been throwing a lot of batting practice, so if he does decide to return for a 23rd season, he likely wouldn't need a lot of time to prepare.
"I don't think I'm going to be too far out of shape if I decide to play again," he said.
Meanwhile the suitors keep calling.
"I've listened to every other team [other than Houston] and I continue to get calls every day from those guys on the teams, front office people, I hear the concerns, I know what's behind it and understand it would be a great story," Clemens said. "It's very flattering [but] it would be a mental challenge [to come back]."
Clemens said he hasn't met with Astros officials.
"I haven't sat down with the hometown team because I can't," Clemens said. "Once I hear from them, I'll put that in the mix if in fact I'm going to crank it up."
The Yankees would love to see Clemens return to New York, but all has been quiet on that front.
"Nothing to report on him, he is retired and he will let us know if he decides otherwise -- if he is interested in us, of course," Yankees general manager Brian Cashman said recently.
Clemens visited with the Red Sox and Rangers on Opening Day in Arlington, Texas. Like the Yankees, the Red Sox and Rangers have made their intentions known to the 43-year-old and are now simply waiting to hear what he decides to do.
Boston's interest in Clemens can only be heightened as a result of the uncertain status of David Wells, who has been battling a knee injury.
The Rangers' rotation is 6-7 with a 4.78 ERA through Sunday's game. Clemens' arrival in north Texas would immediately upgrade the Texas rotation and make the Rangers more of a threat in the competitive American League West, not to mention the additional interest Clemens would generate at the Ameriquest Field.
Should Clemens decide to pitch, it could spark an interesting bidding battle as the two well-heeled AL East rivals and the two Texas teams try to sway the future Hall of Famer. The Astros paid Clemens $18 million last season, the largest single-season contract for a pitcher in Major League history.
Last year, Clemens led the Major Leagues with a 1.87 ERA and helped the Astros reach the World Series for the first time in franchise history.
Houston could be a more attractive option for Clemens than they were during Spring Training. The Astros are currently tied with the Chicago White Sox (13-5) for the best record in baseball. Houston's rotation leads the Majors with a 2.97 ERA, and that's with No. 3 starter Brandon Backe on the disabled list. Rookie Taylor Buchholz has pitched well and left-hander Wandy Rodriguez is 3-0.
"I still keep up with them," Clemens said. "I'm taping Andy's [Pettitte] game, Roy's [Oswalt] game, guys I enjoy watching, so when I'm running around town watching the amateur ballgames, I can check up on the big guys. It's fun to see and I like it when our hitters are smiling."
Clemens is an 11-time All-Star with 341 career victories, the ninth-most in Major League history. He needs one win to tie Tim Keefe for eighth-place on the all-time list.