The 22-year-old, top scorer for the Clarets last season with 26 goals, is out of contract at the end of this term.
Dyche is quoted by the Lancashire Telegraph as saying: "We've always been speaking to [Ings] and his agent.
"That's been going on for months to be honest. That's not a recent thing, it's just an ongoing conversation."
Ings signed a four-year deal with the club when he arrived from Bournemouth for £1m in August 2011.