* Spark says A$2.80-per-share offer undervalues co

* Shares jump to more than 42-month high

* Spark won't allow access to books but open to talks

July 15 (Reuters) - Australia's Spark Infrastructure on Thursday rejected a A$4.91 billion ($3.67 billion) takeover bid by a consortium that included private equity giant KKR & Co Inc, but kept its door open to further talks, sending its shares up nearly 8%.

The second bid from KKR and Ontario Teachers' Pension Plan Board of A$2.80-per-share was 10 cents more than the previous one, Spark revealed.

The electricity poles-and-wires firm is open to sharing "limited information on its business and prospects" subject to a confidentiality agreement, but said the offer did not merit access to its books.

The news sent Spark shares up 7.7% to a more than 42-month high of A$2.67, which is above the first bid but shy of the second. Thursday's offer was at a near 13% premium to Spark's closing price in the previous session.

KKR, in an emailed statement, confirmed making the bid with the Canadian pension fund.

"Overall, we believe the bid prices appear fair and we expect the management to be under increasing pressure to engage further with the consortium, or disclose a better pathway to realising value," J.P. Morgan analysts said in a note.

The offer is the latest in a flurry of deal activity in Australia as record-low interest rates have prompted institutional investors with ample capital to chase higher yields just as the economy enjoys a sharp rebound from a pandemic-driven recession.

A group of infrastructure funds offered $16.6 billion on Thursday to buy Sydney Airport Holdings, which the operator of Australia's largest airport rejected as a lowball bid.

Spark, which operates an electricity distribution network in Southern Australia, has seen its shares rise more than 17% so far in 2021, as infrastructure spending and industrial activity rebound.

Spark is being advised by Goldman Sachs on the buyout offer.

($1 = 1.3367 Australian dollars) (Reporting by Sameer Manekar in Bengaluru, additional reporting by Nikhil Kurian Nainan and Rushil Dutta; Editing by Shounak Dasgupta and Subhranshu Sahu)