The 25-year-old has scored four Premier League goals this season to help propel the Baggies to the Champions League qualification places.
But, speaking to the press, Clarke warned any potential suitors: "Clubs can want to buy Shane, they can come if they want — and the answer is 'no'.
He added, "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.
Long has had some injury troubles, however, but Clarke is optimistic that his striker will be up to the challenge of three games in a week against Sunderland, Swansea City and Stoke City.
"He has got tight hamstrings and we will look after him and make sure he it doesn't become a tear which will keep him out for eight weeks," the Baggies boss continued. "If Shane has to play 90 minutes he can play 90 minutes, no problem."
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