The 22-year-old has scored 10 goals in his first Premier League season but his strikes could not help Burnley beat the drop and their relegation to the Championship was confirmed last week.
Ings has been linked with Manchester United and Liverpool when he becomes a free agent, though any club would have to pay a fee, decided by a tribunal, because he is under 24.
Dyche believes Ings will move to keep playing top-flight football.
"You can never give 100 per cent guarantees. It's probable that was a farewell from Danny though," Dyche said following a goalless draw with Stoke City on Saturday in their final home game of the season.
It appeared to be Ings's final game at Turf Moor in a Burnley shirt, with the striker thanking the fans in the programme and saying an emotional goodbye during a lap of honour.
"It's good to see his development. But it looks like it won't continue with us. He and his agent have put the message out that they are looking at pastures new," Dyche added.
Ings, who moved to Burnley from Bournemouth in 2011, has also been linked with a move to Spanish side Real Sociedad, who are coached by former Manchester United manager David Moyes.
(Reporting by Sam Holden, editing by Ed Osmond)
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