MONDAY, 3:16pm: The Royals are still listening on Broxton but offers haven't been encouraging so far, tweets Danny Knobler of CBS Sports. The Orioles were showing serious interest in Broxton over the weekend, tweets Roch Kubatko of MASNSports.com, though they're showing less interest now. Kubatko says the Orioles are known to want a left-handed reliever but might just be looking to upgrade the bullpen however possible.
SUNDAY, 10:11pm: The Royals are eyeing right-hander Justin Grimm in their discussions with the Rangers, according to Bob Dutton of the Kansas City Star (Twitter link). Evan Grant of the Dallas Morning News echoes the sentiment (on Twitter). Grimm, 23, was a fifth round selection by the Rangers in 2010 out of the University of Georgia. He currently boasts a 1.99 ERA between Double-A and Triple-A and made his Major League debut earlier this season.
6:36pm: The Rangers are also in on Broxton, writes Jon Heyman of CBS Sports. Texas is turning its focus to bullpen help after becoming frustrated with the starting pitching market, according to Heyman.
2:36pm: The Giants have serious interest in Jonathan Broxton, Jim Bowden of ESPN.com and MLB Network Radio reports (on Twitter). Interest on Broxton is picking up and there's a 60-70% chance he'll be traded by the deadline, ESPN.com's Jerry Crasnick reports (on Twitter).
The Giants don't view Broxton as the solution for their bullpen, Danny Knobler of CBSSports.com reported this week. There's not much bullpen help available, now that Huston Street is off the market, Knobler reported today (on Twitter). The Blue Jays and Red Sox aren't selling and teams aren't impressed by the available relievers.
Steve Adams contributed to this post.