Over the last few years, several major sides have reportedly been keen on the Bosnia and Herzegovina international.
And regarding the talk this week of Spanish giants Real contemplating a bid for the 26-year-old, Begovic has been quoted by The Sentinel as saying that, while "very happy" at Stoke, he is "proud to read that sort of stuff" and feels it is "extraordinary to be linked with a club like that".
Hughes, meanwhile, said on Friday: "I'm not sure where the story originates from, but certainly there has been no contact between the clubs.
"But it wouldn't surprise me if there was a modicum of truth in it - that top teams are looking at Asmir - because he is an outstanding goalkeeper.
"We are certainly not encouraging it. Asmir is a huge part of what we are trying to do here."
Asked if he thought Stoke might face a battle to keep Begovic this summer, Hughes said: "Who knows?
"We are very fortunate that he is here and contracted to us. In that regard we have a position of strength.
"But he is an ambitious player and I'm sure he wants at some point to test himself at the highest level possible, in the Champions League."
A player that certainly appears set to leave Stoke this summer is winger Matthew Etherington, signed in 2009 from West Ham, their visitors in the Barclays Premier League on Saturday.
Etherington, who is out of contract at the end of the season and has expressed his certainty he will depart, has played a limited role this term.
The 32-year-old has had a run of substitute appearances lately, though, and Hughes has emphasised nothing has been finally decided in terms of Etherington's situation yet.
Hughes said: "It has been frustrating that he hasn't been as fit as often as I would have liked - he has had issues with his back, and that has caused him other problems.
"But he is fit now and that is why he has been more involved in recent weeks.
"So you never say never, and we are pleased he is an option at the moment."
Twelfth-placed Stoke will face 10th-ranked West Ham, whose manager Sam Allardyce has been named the Premier League's manager of the month for February, without Jon Walters, their latest player to be hit with a suspension.
Both forward Walters and midfielder Charlie Adam are serving three-match bans, with the former's beginning this weekend after an appeal against his red card for a high challenge on Alexander Tettey in last Saturday's 1-1 draw at Norwich failed.
Hughes said on that matter: "We felt it was important we challenged the decision because we felt there was inconsistency there in terms of the same type of challenge happening with other players where it had not been deemed a red-card offence.
"We highlighted three such challenges - one actually involved Tettey, who the week before against Aston Villa had put in a real strong challenge that was more dangerous in my view than Jon's.
"That was deemed to be a yellow card, so we were a little bit confused in terms of what the interpretation of it is."
Hughes will make a late call on whether on-loan Liverpool winger Oussama Assaidi (knee) is ready to return to action, and has confirmed defender Robert Huth will miss the rest of the season after undergoing a second knee operation on Thursday.
Huth has not played for the first team since injuring his knee in November and having surgery soon after.
And Hughes said of the German: ''We tried to get him back and he has been very close on a number of occasions, but unfortunately the knee was reacting adversely.
"So we took him to the surgeon and he recommended Robert had another operation, just to get a real understanding of what is going on in the knee.
"Hopefully he will be fit and well to go for the beginning of next season."