The 33-year-old Savage, also a target for Fulham and Derby, has become disillusioned by life at Ewood Park after starting just one Premier League game since the end of October.
"There has been some contact between our chairman John Williams and Sunderland but my understanding is that the offer is way below the value we place on Robbie," said Hughes.
"If they meet our valuation, I'll look at it, but I won't allow players to leave if I think that it will weaken us.
"We are about to lose Aaron Mokoena to the African Cup of Nations later this week for the best part of a month, so anything that happens in terms of players leaving will be dictated by me.
"But we are always looking at our options and if things present themselves, we will look at it."
Savage has been a frustrated observer in recent weeks.
Hughes added: "Since Robbie has been at the club, he has done a great job for me and he played a big part in keeping us up the season he signed.
"I've tried to explain to him, and everybody in the squad, that there are very few players who go down on the teamsheet straightaway.
"That's the situation we are in now. If you make a disappointed player happy, you then make another unhappy, so you can't keep them all happy at the same time.
"He doesn't take not playing very well."