The 23-year-old will command a fee of around £15m and looks set to break the record fee paid for Wilfried Bony in 2013.
Baston spent last season on loan at Eibar where he scored 18 goals in 36 La Liga games.
Swansea appear to have money to spend at the minute having sold Andre Ayew to West Ham and captain Ashley Williams looks set to join Everton.