United, who had an £8m enquiry for the 21-year-old rejected by Sporting, are preparing to return with an offer of £10m which will be enough to trigger a get-out clause in Veloso's contract when the transfer window reopens in January.
Sir Alex Ferguson's brother, Martin, who is United's European scout, has travelled to Portugal regularly in the two months since Veloso excelled in Sporting's 1-0 Champions League home defeat at the hands of the Reds.
Veloso said: "The best game of my career so far was when we played Manchester United. They are a great team and it is the dream of any footballer to play for such a club."
