The 23-year-old has been linked with a move away from The Hawthorns for the fourth successive window and has not featured for the Baggies since September due to fitness issues.
The Potters have made a formal offer for Berahino this week - thought to be "considerably less" than the £20m bid from Tottenham Hotspur 18 months ago - but Hughes has revealed that he has yet to receive a response.
"Nothing has moved forward from last week. We are still waiting for the player's club to give us an indication," he told reporters. "I think we are looking at players who we feel can improve us, not only short term but long term too, and we have taken that into consideration with this deal.
"It is out of our hands unfortunately, but we are ready to discuss the situation and see where it progresses.
"It has been long-winded, and sometimes you lose some enthusiasm when that happens, but I have learned over the years that you have to be patient.
"I'm hopeful that we'll be able to get something done. We're interested in him, as a number of other clubs are."
Berahino has been at The Hawthorns since the age of 11 and has scored 23 goals for the club in 105 Premier League appearances.