Soto, 29, is hitting .199 with six homers and 14 RBIs in 51 games this season. He was the National League rookie of the year and is under club control for one more season as an arbitration-eligible player.
Brigham is 5-5 with a 3.28 ERA in 21 starts with Double-A Frisco.
The deal has not been made official because MLB must approve the cash exchange, a source said.
Brigham, 24, has pitched in 124 innings this season and has 116 strikeouts and 46 walks. Opponents are batting .260 against him.