The Republic of Ireland international has attracted the attention of other clubs after netting six goals for Premier League highflyers Albion this season.
But Clarke said: "Clubs can want to buy Shane, they can come if they want - and the answer is 'no'.
"I am not going to hype up other clubs and who they should be bidding for. But Shane is our player and he's not going anywhere.
"At the moment he is in a great vein of form. I've run out of superlatives to say about Shane.
"We are delighted with his efforts and I think the competition for places, especially in the forward area, is keeping everyone on their toes and we are the beneficiaries of that.
"Shane's performance last weekend against Chelsea have been like that every time he has been selected this year."