The 50-year-old’s existing terms are due to expire in July but talks have begun over a new deal.
Kenny met Football Association of Ireland chief executive Jonathan Hill last week in England after travelling to watch the Sky Bet League One match between Portsmouth and Sheffield Wednesday.
“We sat down and had a chat, just an introductory chat, so it’s started and hopefully we can progress from there,” said Kenny.
“I don’t see it as any major issue. I’m sure we can move forward and sort it all out.
“It’s a process really and we’re just involved at the start of the process. Talks are ongoing. They’ve just started really.
“I’m involved in the Nations League campaign and I’m pretty certain I will be manager for the European Championship campaign as well.”
Kenny has lost just one of his last 10 games as national team boss following a winless opening 11 fixtures after succeeding Mick McCarthy.
I'm involved in the Nations League campaign and I'm pretty certain I will be manager for the European Championship campaign as well.
His current contract will see him remain in charge of Ireland’s opening four matches of the Nations League next June.
The Irish were on Thursday drawn in Group B1 of that tournament alongside Ukraine, Scotland and Armenia, with their final two fixtures scheduled for September.
Having failed to qualify for next year’s winter World Cup in Qatar, those appointments will be the country’s only competitive outings in 2022.
The qualifying draw for Euro 2024 – which will be staged in Germany – is due to take place in October.
Kenny is also eager to keep his backroom team together, including assistant Anthony Barry – who is also a coach at Chelsea – and goalkeeping coach Dean Kiely, who performs a similar role at Crystal Palace.
“We all love working together and have a great working environment,” said Kenny. “The whole backroom team, the longer we’ve worked together, the better we’ve got.
“As a unit working together, we’d like to keep it intact and that would be the idea. I think they would ideally like to stay on.
“They (Barry and Kiely) are involved in the day-to-day stuff with their clubs so they’re not thinking real long term.
“They both want to stay on board and they’re very much an important part of the set-up going forward.”