The UK's second biggest supermarket chain is currently deciding between three agencies where to place its government relations business, having had TLG on board for four years.
It is understood that the agency shortlist includes TLG.
Like its competitors, Asda faces numerous governmental and legislative issues such as food labelling and food health issues, as well as concern over retail domination by chain stores.
Last month, Asda unveiled plans to create around 5,000 jobs this year in a £500m expansion. The company plans to open 25 stores, refurbish 43 outlets and invest in three new depots in 2012.
The announcement was welcomed by Prime Minister David Cameron, who said it was 'a real boost for the economy and, more importantly, for people around Britain seeking jobs'.
However, the chain's expansion plans could come up against political opposition at a local level.
Asda director of public affairs Allan Edwards confirmed that the pitches had occurred but declined to discuss the matter further.
Asda employs more than 180,000 people and runs 528 stores in the UK. The company, which was bought by the world's largest retailer, Walmart, in 2000, has a market share of around 17 per cent.
Asda appointed former Department of Health director-general for comms Sian Jarvis to lead its comms and public affairs last October. However, this brief is understood to have been launched before her appointment.
Jarvis resigned from the DH in July last year, having been director-general for comms since 2004.
Edwards reports to Jarvis, and has worked at Asda since last January. He joined from Compass Group where he was director of corporate affairs and corporate responsibility.
TLG, led by Michael Portillo's former press secretary Malcolm Gooderham, was brought in by Asda in 2008 after the chain ditched Bell Pottinger Public Affairs.