Miller in high demand

ST. PETERSBURG, Fla. -- With four days before Thursday's trade deadline, left-handed reliever Andrew Miller remains high on the lists of contenders seeking bullpen help. The Braves and Pirates have been tracking him for some time, the Royals have interest, and there were a host of other clubs here for Sunday's finale against the Tampa Bay Rays.

Miller pitched the seventh inning Sunday. He issued a leadoff walk to Curt Casali, then Kevin Kiermaier laid down a sacrifice bunt in self-defense, with Miller coming high and inside with a fastball. The left-hander then retired Desmond Jennings with a called third strike, a fastball at the bottom of the zone, and retired Ben Zobrist on a ground ball to short.

There's a chance that was Miller's last appearance of 2014 in a Sox uniform. A trade could happen at any time.

"I've heard the rumors growing -- I guess they seem to be growing," Miller said. "We're surrounded by distractions [and] trying to filter them out. As professionals, we have distractions every day, all over the place. Find a way to keep them far enough away they don't affect your performance."

Atlanta's only lefty in the pen is rookie Chase Shreve, so Miller is an obvious fit. What could the Braves offer in return? Their top prospect is a pitcher, right-hander Lucas Sims, who is undoubtedly out of bounds in a rental, and they have a 19-year-old left-handed-hitting outfielder in Victor Reyes, who's making his full-season debut this year. They also have a speedy center fielder in Jordan Schafer, who is stuck on the Braves' roster as a fourth outfielder.

The Pirates might make an intriguing match. They have two outfielders, slugging switch-hitter Josh Bell and 2013 No. 1 pick Austin Meadows, who is ranked among Baseball America's top 50 prospects. He is probably too good to include in a trade for a left-handed rental but worth making an inquiry about.

The Royals, who also are interested in Jonny Gomes, have two outfielders, Jorge Bonifacio and Elier Hernandez, ranked among their top 10 prospects by Baseball America.

The Sox might well seek more than outfielders in return; they netted two pitchers for Jake Peavy from the Giants and presumably are happy to stockpile talent anywhere on the diamond.