"We've got MLB Network on. When stuff flashes up, you see it and talk about it," Byrd said.
Leake has reportedly drawn interest from the Blue Jays, who had a scout watching him pitch eight innings for a 4-0 win over the Cardinals on Tuesday. FOX Sports' Ken Rosenthal reported that Leake is among many pitchers still being considered by Toronto.
Another team that had interest in Leake, the Dodgers, reportedly made a trade to acquire Mat Latos from the Marlins. But according to the Chicago Sun-Times, the deal was held up by a medical issue with one of the trade pieces.
Reds general manager Walt Jocketty went back to Cincinnati on Monday after he traded rotation ace Johnny Cueto to the Royals on Sunday for three left-handed pitching prospects. Manager Bryan Price hasn't heard much from Jocketty the past couple of days.
"We've spoken, but very briefly," Price said. "It's been more about things not having to do with trades. In-house business stuff, but not trades."
As for Byrd, he wasn't concerned about the prospect of being moved.
"It's the same. When you're younger, [you worry], but now? No," he said. "I love it here. Nobody wants to go. I'm in a good spot. You do want to win, but I still see a lot of positives here for next year. The offense coming back -- [Zack Cozart] coming back and [Devin Mesoraco] coming back, [Homer Bailey] being healthy and leading the staff. We're piecing everything together, but you still have the core here. If not this year, then next year for us."
The Reds acquired Byrd from the Phillies on Dec. 31. Like Leake and Cueto, he can be a free agent after the season, but he has an $8 million option for 2016 that vests if he reaches 550 plate appearances this season. Until Byrd fractured his wrist and went on the disabled list in June, that option looked attainable.
"I don't think I'm going to be able to reach it," Byrd said. "When I missed those 15 days, it didn't kill it, but it would be very difficult to reach. I can't worry about that. I just have to go out and help this team win games."
Byrd was traded in August 2013 from the Mets to the Pirates after he cleared waivers first. That could be possible for him again this year as he earns the remainder of his $8 million salary for 2015.