The 20-year-old Republic of Ireland international has been on loan at the KC Stadium since November, and Tigers boss Steve Bruce is eager to make his Championship switch permanent.
Bruce, a former Red Devils player himself, is understood to have had a bid accepted by his old club, that could see Brady leave Old Trafford this month, despite additional interest from Watford and Sunderland.
Sir Alex Ferguson is a known admirer of the exciting attacking midfielder, but his lack of first-team football at Manchester United - which has seen him restricted to a four-minute cameo in the Capital One Cup - means that it will probably be best for both parties that Brady continues his trade elsewhere.
The summer arrival of Dutch U21 international Alexander Buttner is also believed to have halted the youngster's progression, despite seeing his stock continue to rise after breaking the Irish U21 goalscoring record last year.
Brady scored one goal in 12 appearances for Hull, before returning to Manchester United earlier this week. But, he now looks set to rejoin the Tigers and help them in their push for promotion back to the Premier League.
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