The 60-cover bar and eatery on Argyll Street in the Scottish city is set to open its doors in May. The opening will be the culmination of three years’ work for the duo since they first met when McKenna was actually planning to move to Australia.
Speaking to BigHospitality, the chef said he had become disillusioned with the UK dining scene and, spurred on by Stein, decided to take the plunge and go into partnership to open his own restaurant.
"I didn't really see anywhere in Glasgow that I wanted to work and there was nothing exciting for me to get my teeth into," he explained. "I couldn't imagine opening a restaurant by myself but the two of us with our different skillsets - it really clicked."
The restaurant itself will be located in a Grade II-listed, 108-year-old, former tenement building which has lain empty for the last eight years after previously operating as a shop although a restaurant license had been acquired for the site in the past.
The venue was not the pair's first choice - they were gazumped by a chain on one location and the financing fell through on three others - but McKenna believes they have ended up with the best setting for their restaurant concept.
"We went hell for leather when we first came up with the idea and we got a site and what we thought might be a pretty good opportunity but the funding fell through at a crucial stage. The site we have got now, I must say, is a lot better - area-wise and aesthetic-wise.
Gannet will serve diners in an area of the hospitable city known for its burgeoning restaurant scene. It will be located close to a number of independents, museums and galleries and The Hydro arena.
The restaurant itself will showcase fine-dining food but 'without the fuss' - a reference to both cooking style and service.
The pair have spent the last few years touring Scotland to meet local producers in order to source as many of the ingredients direct from sustainable sources - for example they have found a deer stalker on the Isle of Bute and are hoping to buy a half carcass of venison from him for a week of specials.
The majority of mains at Gannet will all cost less than £20 and there will also be a bespoke bar menu alongside the small set menu and a wide range of specials.
"We want our customers to come back and feel like they are getting something new, fresh and original," said McKenna. "Whether it is the following week or two weeks later, we don't want to be having to do a certain dish again and again."
McKenna trained in Donegal before stints with Hawksmoor's Richard Turner, at Chez Bruce and as a personal chef for a Saudi prince and a Russian businessman. Meanwhile, Stein's career includes periods as a banker and a civil servant before making the move into restaurants, cooking for free before moving to Scotland to work for Tom Kitchin, Martin Wishart and, most recently, Michael Caines.
The duo have put their own funds into the project and are supported by a business partner alongside a small, but crucial, tranche of bank funding.
"This is a dream come true," McKenna explained. "It is our opportunity to stand up and be counted. If we can open the restaurant, make a few pounds and make people happy, we will be very happy," he concluded.