The Bosnia-Herzegovina international will enter the final year of his current deal this summer and there has been much speculation about his future.
Hughes has often stated that club and player plan to discuss the situation at the end of the season, but that has not prevented rumours that talks have stalled over wage demands.
Begovic has also been linked with Manchester United and Liverpool recently, with stories fuelled by the player's lack of participation in the Potters' last two games.
Hughes says he has been fulfilling a pledge to allow England Under-21 international Jack Butland some game time late in the campaign, but he admits Begovic asked not to be on the bench.
The 27-year-old instead took the opportunity to undergo what Hughes described as a "slight procedure", but he could be back in action at Burnley in the Barclays Premier League on Saturday.
Hughes said: "My view on it hasn't changed
I want Asmir to stay here
We can offer him a good option
We feel we are progressing and we want him to be part of that.
"We are conscious that he is in the last year of his contract, so we are wary of that.
"Financial demands will always be part of the discussion, but I don't think that would be something that would affect anything we would be looking to do with him.
"We haven't had those talks yet but once we do at the end of the season then hopefully we can get a quick and happy resolution.
"We want Asmir to keep progressing as one of the best goalkeepers in the Premier League here
I am very hopeful of being able to agree something with him and his representatives."
The Potters head to Turf Moor having equalled their Premier League-best points tally of 50 with last week's 3-0 win over Tottenham.
One more point will not only set a new club record but ensure successive top-half finishes in the top flight for the first time in 40 years.
Hughes, who will have been in charge at the Britannia Stadium two years this summer, believes the club have made good progress during his tenure.
He wants that to continue and sees no reason why the club should not be aiming to qualify for the Europa League again in the near future.
"We have two games to hopefully exceed what we achieved last season, starting with the one against Burnley," the Welshman said.
"I have a real good feeling about this place and feel there is even more room to progress for us
I would love to take the club into Europe if possible - that is an obvious target for us.
"People suggest that being in the Europa League is a burden, but for ourselves it is a burden we would be more than happy to take on."
Source : PA
Source: PA