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It is not clear how close the New York-based private-equity firm is to a deal for Kinetic or if it faces any rival bidders, the Journal said.
A spokesman from KCI said the company does not comment on rumors and speculation.
If a deal is reached, it would mark one of the largest leveraged buyouts since the financial crisis.
Private equities have shied away from such big acquisitions lately, but Blackstone has recently reached a $16 billion new buyout fund, which is one of the largest of its kind on record.
Shares of Kinetic soared nearly 13% to about a six-year high of $67.38 just before the markets close on Wednesday.