Tim Kurkjian gives the latest details on how close the Cubs are to trading for Aroldis Chapman but explains that other teams could still get involved. (1:05)

CHICAGO -- A trade that would send New York Yankees closer Aroldis Chapman to the Chicago Cubs for Class A shortstop Gleyber Torres is close to completion, according to multiple sources familiar with the trade.

Chapman, 28, would fill an immediate need in the Cubs' bullpen, as the team lacks a true left-handed, late-inning reliever with his kind of experience. Chapman is 3-0 with a 2.01 ERA and 20 saves for the Yankees, after he served a 30-game suspension under MLB's domestic violence policy earlier this season.

Chapman has 166 saves over a seven-year career, most of which were with the Cincinnati Reds.

The Cubs and Yankees are in talks to send pitcher Aroldis Chapman to Chicago in exchange for top-rated prospect Gleyber Torres, according to multiple sources familiar with the negotiations. Al Bello/Getty Images

Torres, 19, would be the centerpiece going back to the Yankees. He is the Cubs' top-ranked prospect and No. 15 in baseball, according to ESPN baseball insider Keith Law. Torres was scratched about 20 minutes before first pitch Sunday afternoon but was seen in the dugout throughout the game while the trade, which involves other players, was being worked on.

The Cubs traded for lefty Mike Montgomery from the Seattle Mariners on Wednesday, although he gave up a home run to the first batter he faced with his new team Saturday. They also added six-time All-Star Joe Nathan to the roster Sunday. He earned his first win since September 2014 by striking out the side in the sixth inning of the Cubs' 6-5, come-from-behind win over the Milwaukee Brewers.

It's not clear when the deal for Chapman -- if it's completed -- will be announced. He is set to become a free agent after this season.