The 23-year-old striker almost joined United on transfer deadline day at the beginning of this month but the deal did not go through in time.
"He can go for a maximum of 93 days and I think Leeds want him for the play-off final should they reach it," Rams boss Nigel Clough said.
"Working back from there, I think he can start on February 21 so it should all get sorted out this week."
Dickinson was signed from Stockport last summer for a fee of £750,000 by former Derby boss Paul Jewell but was loaned out to Huddersfield at the start of the season.
He also had a loan spell at Blackpool before the turn of the year when Simon Grayson was their.