The Telegraph, citing sources, reported late on Friday that the U.S. private equity firm had attempted to jumpstart proceedings to buy Viridor earlier in 2019 but was rejected by Pennon.
London-listed Pennon shares jumped as much as 10.4% on the day and by 1555 GMT were trading at an all-time high of 10.8 pounds.
Pennon in September said it would conduct a review of its strategic focus, growth options and capital allocation policy given the strong performance of Viridor and its utility business South West Water.
"The review is ongoing and all options are being considered. We will update the market as and when it is appropriate to do so," a company spokeswoman said in an e-mailed statement to Reuters on Monday.
KKR declined to comment on the report.
(Reporting by Muvija M and Pushkala Aripaka in Bengaluru; editing by David Evans)