In return, the Giants will receive two prospects from the Yankees, including Triple-A shortstop Abiatal Avelino, according to the New York Post.
If the deal goes through before the end of Friday, McCutchen will be eligible for the Yankees' postseason roster.
McCutchen, the 2013 National League MVP, is a free agent at the end of the season. He was owed $14.75 million this season, with roughly $2 million of that remaining to be paid.
The 31-year-old was acquired by the Giants from the Pittsburgh Pirates during the offseason and has hit .255 with 15 home runs, 55 RBIs and 13 stolen bases in 130 games this year. He spent the first nine years of his major league career with the Pirates, rebuilding his value with a 2017 campaign that saw him hit .279 with 28 home runs and 88 RBIs.
McCutchen was a five-time All-Star from 2011-15 and won the MVP when he batted .317 with 21 homers, 84 RBIs and 27 steals in 2013. He finished third in the vote in 2012 and '14 and fifth in '15.
McCutchen came into the league as a center fielder, though he has exclusively played right field this season.
The Yankees were said to be seeking outfield upgrades ahead of the July 31 non-waiver deadline but were unable to make any big additions. The team's depth at the position has been tested with Aaron Judge on the disabled list since July 27 with a chip fracture in his right wrist.
Following a loss to the Detroit Tigers on Thursday night, the Yankees are 84-50 and 8 1/2 games back of the Boston Red Sox in the American League East. New York holds a four-game lead over the Oakland Athletics for the No. 1 wild card in the AL.
--Field Level Media