James Shields

The Angels’ AL West-rival Rangers as well as their crosstown-rival Dodgers have joined the trade talks for Rays starting pitcher James Shields, according to CBSSports.com’s Jon Heyman.

Heyman said that all three teams have proposed trades to the Rays, but Tampa Bay is looking for a more enticing offer. He also reported that the Angels discussed a package including young center fielder Peter Bourjos, who hasn’t played much because of the emergence of sensational rookie Mike Trout.

According to Heyman, the Rangers also are interested in Zack Greinke and Josh Johnson, while the Dodgers remain high on Ryan Dempster and possibly Matt Garza as well.

Shields, 30, has a $9 million team option for 2013 and a $12 million team option for 2014. He’s 8-6 with a 4.39 ERA this season.