An image on the Ryanair website shows the proposed new seats, which McNamara told marketwatch.com would make room for as many as 50 to 60 additional passengers.
However he conceded gaining approval to install such seats could take some time, with a pilot programme not expected for another three years.
"Ryanair will continue to explore the concept of 'fare free standing' flights with Boeing and the relevant aviation authorities in the US and EU," McNamara wrote in a statement on the airline's website.
The Irish carrier is not the first airline to propose standing in-flight.
Last month, Chinese news website CCTV reported that Chinese carrier Spring Airlines was considering making a submission to the aviation authority requesting permission to install upright seating.
"It's just like bar stools. The safety belt is the the most important thing. It will still be fastened around the waist," Spring Airlines' Zhang Wuan told the website.
In 2006, the New York Times reported that Airbus had researched the idea of upright-seating in 2003, but had since abandoned it.
Ryanair is no stranger to controversial ideas.
In April it announced plans to introduce a 'fat tax' after an online poll showed 29,000 people would support such a move.
That plan was scrapped in May after Ryanair said there was no way to collect the tax without disrupting its 25-minute turnaround times and its online check-in processes.