The 20-year-old signed a four-year deal with The Red Devils after seeing out his deal at the Stadium of Light on Monday.
Despite technically leaving on a Bosman free, The Black Cats have asked for a tribunal to determine the amount of compensation they are entitled to receive for the youngster.
"The club has made a formal application to The Football League to request a date for a tribunal hearing to discuss compensation with regard to David Bellion's transfer to Manchester United, which was confirmed yesterday," A Sunderland spokesman told the club's official website.
Fifa rules state that the Wearsiders are entitled to compensation from United for an out-of-contract player who is under 23 years of age, which in this case is Bellion.
Meanwhile, Black Cats chairman Bob Murray has reiterated his belief that some of the club's players will be moving on before the start of the new season.
Murray was adamant that unwanted squad members will be moved on, despite the slow progress in the transfer market so far.
Manager Mick McCarthy saw many familiar faces at the start of pre-season training on Wednesday, as the club struggled so far to gain the interest of other clubs for players deemed surplus to requirements.
However, Murray believes the next few weeks will see more transfer activity and that McCarthy will be able to shape his squad more to his liking before the August 9th opener at Nottingham Forest.
"We've had a lot of interest and conversations about our players but the transfer market has started slowly and so far there has been very little activity across the board," revealed Murray.
"However, most managers return for pre-season this week and are likely to start speaking to one another.
"The situation at Sunderland has not changed. There are players that Mick wants to stay, and some individuals that want leave, but they also have to find new clubs.
"And there are also players who have been told that their time is up at Sunderland.
"However, until any players leave the club we must ensure they keep their fitness at a peak and therefore they have been told they are required to return to the club and take part in pre-season training."
