The US president's campaign said a financial trust associated with Mr Romney had money in a Goldman Sachs fund and in other accounts in Ireland.
Ireland was listed by the Obama campaign as having a tax rate of 12.5pc.
"The Taoiseach's office was contacted by Governor Romney seeking a meeting. Arrangements for that are being finalised at the moment," a Government spokesman said.
The meeting will take place in London city centre, possibly at the Irish Embassy.
Mr Romney and Mr Kenny are both expected to attend the opening ceremony of the London 2012 Olympics.
The presidential election nominee will meet with the US Olympic team and attend the 2012 Olympics.
Mr Romney's wife, Ann, owns a horse that will be competing in the Olympic dressage competition.