United will pay Fiorentina 10m Euros (£8.5m) to sign Amrabat on loan for the season, with an option to buy the Morocco international for 25m Euros (£21.4m), according to Sky Sports News.
The 26-year-old Reguilon will arrive as a replacement for Luke Shaw, who will be sidelined for several weeks after sustaining a muscle injury last month. Back-up left back Tyrell Malacia is also sidelined due to an injury he picked up last season.
Earlier today, Manchester United signed Turkish goalkeeper Altay Bayindir from Super Lig side Fenerbahce on a four-year deal, with the option of a further year, a day after Dean Henderson joined Crystal Palace.
United, with two wins from three league games, travel to face Arsenal on Sunday, with the Gunners sitting one point ahead of them in the table.