Clarke, 22, arrived at Stadium of Light from Tottenham Hotspur last year and has already established himself as a cornerstone at the Championship outfit.
His noteworthy performances last year have drawn interest from several sides and Burnley have been keen on securing the services of the winger.
The Clarets are eager to stay afloat in the Premier League next season and have witnessed a flurry of transfer activity at Turf Moor.
The Lancashire side are known to be admirers of Clarke but have seen several bids for him turned down by Mowbray’s side.
And the Sunderland boss is now feeling that the Clarets have given up on snapping up the Englishman and are now looking at other options.
“Every player has their price and so it would be silly for me to sit here and say any player is not for sale, because everyone is at the right price”, Mowbray was quoted as saying by the Sunderland Echo.
“But I’d have to say that it feels to me as if Burnley have been moving away and are looking at other options, choices.
“As far as I can see they were testing the water and as far as I’m concerned, the right decision has been made.
“You can see right through pre-season that Jack Clarke is ultra confident at the moment, right at the top of his game.”
Clarke has still three years remaining on his contract with Sunderland and the Black Cats are hoping to see him deliver more moving forward, with the Championship side eyeing returning to the top-flight next term after a hiatus of six years.