Four teams -- the Astros, Rangers, Red Sox and Yankees -- are in the bidding for Clemens' services. All four teams have been in contact with Clemens' agents, Randy and Alan Hendricks of Houston. The Hendricks met with Houston owner Drayton McLane Jr. and Astros general manager Tim Purpura last week.
Clemens hasn't decided if he will pitch again or which team he will choose if he does return.
"I'm listening to what the Hendricks have to say," Clemens said. "They'll come over and meet with me again this week. They're doing it about once a week; giving me updates from all the teams. I am going to have to make a decision if I want to play this year fairly soon."
Randy Hendricks has previously indicated his client will likely make a decision by June 15.
"I would say that's a pretty good date," Clemens said. "For me to be ready I would think I would probably have to give somebody an answer a little bit before that maybe."
Sources indicated Houston's offer is $20 million annualized, or approximately $11.67 million assuming Clemens returns on June 15.
Clemens would not discuss terms but did say the Astros are hoping to have the flamethrowing righty back in the rotation by the middle of next month.
"Tim and Drayton gave me two dates they would like if I do choose to be back, they would like me back by," Clemens said. "So there are target dates out there and they're in June."
Clemens said he didn't remember the exact dates.
"I just know they're in mid-June," he said.
The Astros are scheduled to play the Chicago Cubs at Wrigley Field from June 13-15, but open a six-game homestand on June 16 with three games against Kansas City followed by three against the Minnesota Twins. If Clemens decides to come back to Houston later in the month, the right-hander could get another crack at last fall's World Series opponent, as the Astros are scheduled to face the Chicago White Sox at U.S. Cellular Field from June 23-25.
Clemens, wearing an Astros jersey and a cap with the Major League Baseball logo on it, gave the interview at the Musical Scores Education Outreach Program put on by the Center for the Performing Arts at The Woodlands, a community north of Houston. Musical Scores primarily serves at-risk underprivileged middle school students who must earn the chance to attend.
"I've got four boys, my oldest one is 19, my youngest one is nine," Clemens told the students. "I'm just a Dad to them, that's the best thing. I'm not the Rocket, I'm not the guy who plays for the Houston Astros sometimes."
Clemens led the Major Leagues with a 1.87 ERA last season while helping the Astros reach the World Series for the first time in franchise history.
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.