Governor Ernie Fletcher announced the date for the special session, but the call has not been made.
House Speaker Jody Richards says a special session would be a waste of taxpayers' money.
Fletcher's main focus for calling the session is to bring more energy projects to the state.
There are four companies considering Kentucky as a site for building alternative fuel facilities.
Governor Fletcher says the General Assembly needs to make a move now to make those projects financially feasible rather than wait until January.
Richards says Fletcher hasn't provided enough details to justify calling a session, which costs taxpayers $60,000 dollars a day.
"You and I pay for that. I"m not in favor of having special sessions unless there's a real emergency. They're called extraordinary sessions, the reason should be extra-ordinary", says Richards.
Governor Fletcher also mentioned funding university construction projects if the special session happens on July 5th.
Although Fletcher didn't get specific, offering health insurance to domestic partners through public universities has been a big issue this year.
Funding to match a federal grant for runway improvements at the Blue Grass Airport may also be on the agenda.
The Blue Grass Airport was the site of the 2006 Comair crash that killed 49 people.