The 19-year-old is expected to leave Old Trafford before next Monday's 11pm deadline in search of regular first-team football.
Romano also states that United's interim boss Ralf Rangnick has approved the transfer, which is set to be finalised in the next few hours.
Rangers are set to beat a host of interested clubs including Feyenoord to the signing of the Ivory Coast international, who could be viewed as a direct replacement for Ianis Hagi, who is ruled out for the rest of the season with a knee injury.
Diallo has featured only nine times for United's senior side across all competitions since he arrived from Atalanta for around £27m in January last year. body check tags ::