Brady had spent the past two months with Hull and scored once in 12 appearances before returning to Old Trafford earlier this week.
Tigers boss Steve Bruce had been keen to agree a deal to bring Brady back to the club, either on another loan or permanently, and now appears set to secure the 20-year-old's signature.
It is understood Hull will pay a fee in excess of £2million for the Republic of Ireland international, who also spent last season on loan with the Championship club.
Brady has made just one senior appearance during his United career when he featured against Newcastle United in the Capital One Cup earlier this season.
He could be joined at Hull on a long-term basis by another player who has impressed on loan after Bruce agreed a £1.5million fee with Sunderland to sign midfielder David Meyler.
Bruce is keen to strengthen his squad in the January transfer window to maintain the Tigers' push for promotion back to the top flight, with his side currently in second position, two points clear of third-placed Crystal Palace.