The Whites have spent several weeks monitoring striker Mikael Forssell on trial, and The Sun reports that Grayson is set to hand the Finnish forward a deal until the end of the season.
A free agent following his summer release from Hannover 96, Forssell is expected to sign a deal with the club before the weekend clash against Crystal Palace.
The same report goes on to claim United will look to sign Stoke City full-back Danny Pugh on an emergency loan when the window opens later today.
28-year-old Pugh, a versatile defender who can play in midfield, will provide the Leeds United boss with some much-needed strength-in-depth.
Pugh became the first player signed under then boss Kevin Blackwell in a deal involving former Leeds favourite Alan Smith to Manchester United, making 50 appearances and scoring 5 goals between 2004-06.