"My understanding is that the prime minister's schedule will not allow that to happen and I am not in control of that schedule.
"Obviously, when details are absolutely finalised, we will be aware of those," Kenny told lawmakers.
Dublin is yet to confirm the precise date for next week's visit, during which Kenny will hold a meeting with the British prime minister.
The invitation to address parliament was sent to May's office earlier this month, following earlier confirmation of the one-day visit to discuss the implications for both countries of Britain's decision to leave the European Union.
Finances will also likely be discussed during the bilateral meeting, as Britain is the country's single biggest trading partner.
Had May accepted Kenny's invitation to address parliament she would have been the second British prime minister to do so, after Tony Blair in 1998 after the signing of an historic peace accord in Northern Ireland to end three decades of violence.
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