The bullpen is a focus for the Braves, sources say. Coppolella repeatedly has said that the team is intent on improving upon its 67-95 record from last season.
O’Day, viewed by many as the top reliever on the open market, is seeking a four-year deal between $28 million and $36 million, sources say.
The Dodgers are among the other teams pursuing O’Day, who had a 1.92 ERA and .580 opponents’ OPS with the Orioles the past four seasons.
The Braves likely view O’Day as a potential closer. Thornton, 39, is coming off a strong season with the Nationals and would serve in a setup role if the Braves signed him.
Criticism of the Braves’ approach mounted after the club traded shortstop Andrelton Simmons and talked about deals involving first baseman Freddie Freeman, according to FOX Sports and other outlets.
Coppolella since has said that he will not trade Freeman. The Braves also have discussed ace right-hander Shelby Miller with other clubs, but in at least one of those conversations attempted to acquire major-league talent.
The Diamondbacks, sources say, balked when the Braves’ request for Miller was a player who is part of their major-league core — possibly center fielder A.J. Pollock, who, like Miller, has three years of club control remaining.
“If we truly were going to tank, we wouldn’t have had (shortstop Erick) Aybar come back in the (Simmons) trade,” Coppolella told USA Today. “If we were trying to tank, we wouldn’t have signed (catcher) A.J. Pierzynski. If we were trying to tank, we would have traded (Cameron) Maybin at the deadline last year, and we had plenty of offers.
“We want to win. And we will win. I’m not under any delusions that we’ll win 110 games, but we’re not going to lose 95 games again. We will win more games than we did last year.”