Speaking before the opener of a three-game series against Houston, Anthopoulos said he's currently immersed in preparation for next week's draft but is starting to "engage a little bit more" in trade talks.
"If there is a bullpen piece out there, we'll look to do something," he said during a wide-ranging 15-minute media availability. "I know there's been reports about us inquiring about guys and that's fair to say. I wouldn't deny those."
Anthopoulos also confirmed that veteran free agent reliever Rafael Soriano is a player who interests him.
"I think it's fair to say," he said. "I normally don't comment specifically about players but that one I think is someone that we'll look into. I think it's stating the obvious there."
Soriano spent the past two years with Washington and has yet to play this season.
The Blue Jays took a 25-30 record into Friday night's game against the Astros. Despite the early struggles, Toronto remains in the thick of the American League East race.
"The division is wide open," Anthopoulos said. "It goes without saying none of the teams have really run away with it. You've got Tampa and New York that are obviously ahead right now but we're all in it because of the play of the division."
Entering Friday's games, Toronto was 4 1/2 games behind the first-place New York Yankees, who were a half-game up on the Rays. Toronto was in a virtual tie with Baltimore, one game ahead of last-place Boston.
Two glaring team statistics that jump out are the Blue Jays' 3-12 record in one-run games and 11-18 mark on the road.
"There's been a lot of one-run games that we haven't been able to pull through," Anthopoulos said. "The analytics guys will tell you in one-run games, there is a significant element of luck. Other people may not agree. I don't know where I fall into that.
"But I think when I look at the club overall and I look at the division and where we're positioned and the upside, I still think we've got a very good team and a chance to make a run."
There have been some recent signs that the Blue Jays may be close to turning things around.
Slugger Jose Bautista has returned to right field, significantly improving the outfield defence and freeing up others to be slotted into the designated hitter spot he occupied while nursing a sore shoulder. The starting rotation has looked much better and the team's offensive numbers have remained strong.
However, team defence has been suspect, there is no real closer on the staff and inconsistency has plagued the bullpen. Toronto is last in the major leagues with six saves and owns an AL-worst earned-run average of 4.41.
Catcher Dioner Navarro, who has been relegated to a backup role with the off-season addition of Canadian Russell Martin, could be an attractive trade target for teams.
"I think I'm stating the obvious here but behind the plate with Navarro, that's an area of depth," Anthopoulos said. "We're not hiding anything there. He can be an everyday guy for somebody so that's an area. Look, we like him on the team. I've said this, he's valuable. We're proud that he's on this team.
"But if there's that opportunity where we improve the club and it gets him an everyday playing spot, we would do that and I've told that to him."
After the weekend series against the Astros, the Blue Jays will continue their six-game homestand with a three-game set against the Miami Marlins.
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