Chairman Michael Johnston has told BBC Sport he is ready to meet an un-named party to discuss a business proposal.
Johnston said he had been approached by a third party and had planned to meet the individual, but was dismayed that the approach had been leaked so early.
"Only a few people knew about the approach. It is concerning that someone has leaked the details," said Johnston.
An unidentified Kilmarnock fan who regularly attends matches at Rugby park is thought to be behind the move for the club, which has debts believed to be around £10m.
Johnston says the club had reduced its debts by around £2.5m over a three-year period and was now showing a profit.
"I have increased spending by around £400,000 on wages and we have spent money on refurbishing two of the stands at the stadium as well as upgrading software," Johnston added.
"This move is at a very tentative stage. I have no idea what this individual's plans are.
"As Kilmarnock chairman and a lawyer my job is to consider all approaches offering investment, but I have to be very careful of the kind of individual who may wish to invest in Kilmarnock given all the recent publicity surrounding gambling syndicates and money laundering in football.
"I will act solely in the best interests of the club."