There has been talk this week that United, whose youth set-up Shawcross was part of before he moved to the Britannia Stadium in 2007-08, have been looking at the 27-year-old as a potential January transfer window signing.
But speaking at his press conference to preview Sunday's home Barclays Premier League clash with Swansea, Hughes said: "I'm not sure where that originated from - I think somebody told me it might have come from America at some point.
"There's been no contact and I don't expect there to be any, and we wouldn't encourage any contact anyway.
"Ryan is very settled here, he is the captain of the club and we have no intention of allowing him to leave.
"He's a big part of what we want to do in the future."
Another Stoke player who has been in the news this week is Peter Crouch, with the 33-year-old striker expressing his desire to extend his stay with the club beyond the end of his current deal next summer.
Crouch, who like Shawcross has been left out of the England set-up for some time, has scored three goals so far this term.
And Hughes is keen to keep the tall frontman
When asked about how discussions were going on that front, the manager said: "We spoke briefly.
"I think Peter is one of those players who is quite unique in what he offers, so you can see the attraction that other clubs maybe have in terms of bringing him to them.
"We value Peter and we would certainly like him to stay if we can come to some agreement because he does give us a different type of threat and one that opponents find really difficult to cope with.
"We are hopeful there will be some common ground and that we'll be able to progress.
"It's still very early in discussions to be honest and Peter is in quite a strong position in terms of going into the last year of his contract.
"But I sense he is really happy here, and that he enjoys the work he gets and playing with the players he has around him.
"All those things will be taken into account I'm sure when a decision is made."
Hughes expects forwards Victor Moses and Mame Biram Diouf to be back available for Sunday's match but also has fresh injury concerns.
Moses, who came off in the 3-1 loss at Sunderland on October 4 due to a thigh problem, and Diouf, absent from the game because of a hamstring complaint, have both trained for the last couple of days.
However, midfielder Glenn Whelan looks set to miss out having picked up a knee issue playing for the Republic of Ireland, forward Marko Arnautovic will have to shake off a hip injury sustained on Austria duty if he is to feature, and defender Robert Huth is a doubt with a calf problem.
On Whelan, Hughes said: "We have a big worry over Glenn unfortunately.
"He had to come off in the international match and is going for scans today just to get a real, understanding of what's going on.
"He took a big bang on his leg and is in a lot of pain at the moment, so we need to get the bottom of that."
Source : PA
Source: PA