Both companies have approached timber supplier Finnforest Merk to design, supply and install the wooden components for the new eco-friendly supermarkets.
Retailing behemoth Tesco is hoping to apply the timber construction methods to a new store in Wick, Scotland, where glulam is being considered for the structural and load-bearing elements of this scheme, as well as the panel systems for the building envelope.
Meanwhile Asda is talking to Finnforest about two new supermarkets - one an Aedas-designed scheme at Bootle in Merseyside, the other at Shaw near Oldham.
Warren Dudding, marketing manager for Finnforest UK said: 'These potential projects demonstrate the retail sector's concern over delivering on sustainability.
'Timber construction is an obvious choice for any organisation planning an environmental and sustainable scheme and as a material it can work with other areas of a building's infrastructure and organisational operations, such as lighting, heating and distribution, to move closer to a state of carbon neutrality.'
However, eco-architect Bill Dunster, the designer behind the famous BedZed development, thinks the move is little more than good marketing.
He said: 'It would be hugely better for the environment if the same supermarkets sold local organic produce in brown paper bags and engaged with the food-miles and sustainable agriculture movement, rather than promoting the superficial 'wood is good' green-wash.'
Dunster went on to question the benefits of using an entirely wood structure in terms of C0 2emissions. He said: 'Passive cooling with radiant thermally massive interior surfaces would probably have reduced lifecycle carbon emissions.'