United are chasing the Portugal international, who admits: "My dream is to play in the Premier League and, if possible, for Manchester United. That is not a secret, even though I'm 100 per cent a Sporting Lisbon player at the moment.
"I will wait for the end of the season for any solution to what has been happening and see if an offer finally arrives. But to play for this club would be sensational. It would be nearly impossible for me to reject this option.
"From my time with Portugal I have heard from Cristiano and Nani about what a club United is. Any player would be happy to play there.
"I am still young and I believe that I will arrive in the Premier League one day."
Queiroz admitted United manager Sir Alex Ferguson is a fan of the player but suggested there may not be a place for him in the team who have already qualified for the second stage of the Champions League with two games to spare.
Queiroz said: "It is impossible to ignore good players and we are following the development of some Portuguese players. One is Veloso. It would be ridiculous not to. Players like Veloso are on the list but maybe not a priority at the moment.
"If Scholes, Michael Carrick, Owen Hargreaves or Anderson leaves the club one day then it is true that a player like Miguel Veloso would be a priority."
Ahead of tonight's clash, Veloso added: "This match is decisive for us in terms of our future in Europe this season.
"From my personal point of view, I do not need to prove anything to the English. Veloso is the same player in each match and I do not try to reach a superior level in one particular match.
"Queiroz spoke about me in the papers in a good way and that is important, but at the moment I'm at Sporting and the question about a move to United is only a possibility."