The 33-year-old, who scored his 25th Premier League goal for Stoke in Saturday's 2-2 draw with Queens Park Rangers, is out of contract next summer.
"We've had conversations about that," The Sentinel quotes Hughes as saying. "Peter knows how much value I place on him, not only on the field, but also off it.
"Everybody enjoys his personality and his company, so that's something we are mindful of and you don't allow that to leave your club lightly."
Crouch signed for the Potters from Tottenham Hotspur in 2011.