Ings’ current four-year contract expires at the end of the Premier League season.
Dyche admitted the 0-0 draw with Stoke City in the final home game of the campaign was likely to be the last for Ings at Turf Moor.
But he insisted the club was in a strong position to try and retain the services of the nucleus of the squad in next season’s Championship.
He said: “You can never give 100 per cent guarantees. Obviously Danny is the outstanding one, but we are in a good place financially and most of the players are under contract, so we think we are in a strong position and there is certainly no thought from the club about shipping out players, that’s for sure.
“It’s probable that was a farewell from Danny though. The sounds coming out of him and his agent make it probably that we will be going elsewhere.
“There is a kind of message going out that they will be looking for pastures now. That’s sometimes happens in football and every player has the right to run their contract down if they want to, so we will see what happens in the summer.”