McCutchen will be a free agent after the season.
The Yankees could use another outfielder and have never been shy about bringing in big names.
In return at this time, the Giants are getting infielder Abiatal Avelino and one more prospect yet to be named, and multiple reports have stated that no formal announcement on the entire deal will come until Friday. Had he been claimed, San Francisco would've only been able to trade him to the claiming team within 48 hours.
The 31-year-old McCutchen has been the Giants' regular right fielder.
Avelino, 23, has split the 2018 campaign between double-A Trenton and triple-A Scranton/Wilkes-Barre in the Yankees' farm system, combining for a.287 batting average (133-for-464) with 65 runs scored, 13 doubles, eight triples, 15 home runs, 66 RBI and 25 stolen bases in 122 games.
He could fill that spot for the Yankees, who have been missing slugger Aaron Judge since his wrist was broken by a pitch in late July.
McCutchen is in the final year of the six-year, $51.5 million contract he signed in March 2012.
De Paula, 20, has spent all of this season with short-season Staten Island in the New York-Penn League, going 2-2 with a 1.71 ERA (9er, 47.1ip) in 10 games (nine starts).
McCutchen must be on the Yankees' roster by September 1 in order to be eligible for the postseason roster.
McCutchen, who was traded to the Giants in the offseason, is hitting.255 this season with 15 home runs and 55 RBIs.