Mourinho's appointment is expected to be confirmed after the 53-year-old Portuguese meets with senior United officials on Tuesday, BBC News reports.
It is not yet certain what future Ryan Giggs, Van Gaal's assistant, has at Old Trafford or what will happen to the rest of the coaching team.
BBC Sport reported on Saturday that United's FA Cup win over Crystal Palace would be Van Gaal's last game in charge.
Read alsoCeremony held in Kyiv before National football team sets off for Euro-2016 in France (photo, video)Saturday's FA Cup success at Wembley gave United a first trophy since Sir Alex Ferguson delivered the Premier League title in 2013 in his last season before retirement, but it was not enough to stop Van Gaal from losing his job.
Mourinho was sacked by Chelsea last December, just seven months after leading the London club to the Premier League title.
