The 19-year-old is still to make his debut for the Blues and it appears United have stepped in to sign the defender. Whilst there has been no official comment from the Red Devils, it is thought the player has undergone a medical.
And his agent, Adam Bouskouchi - while not indicating where Veseli was heading for - did advise that news could be expected "very soon" on his Twitter account.
It is not known at this stage whether United manager Sir Alex Ferguson would regard Veseli as a member of his first-team squad.
However, beset by injuries at the moment, Veseli would be a useful addition.