Friskney’s closed last September after trading for more than 100 years in the town.
Since the closure, the future of the site has been subject to intense speculation.
Many people are claiming it could be bought by either Aldi or Lidl.
Both stores have previously confirmed they are considering Horncastle as a potential location.
However, sources have told the News that neither company has expressed serious interest in the Friskney site.
Town Mayor Coun Fiona Martin said she was ‘not aware’ any new planning applications had been submitted.
She accepted the land could ‘tempt’ retailers - and house-builders - but stressed access and an increase in traffic were potential stumbling blocks.
Coun Martin said: “Everyone is aware of the (traffic) issues that we already have in West Street.
“While I’ve no doubt the site is large enough (for a supermarket)it would only add to the existing issues.
“I think a lot of people would be concerned.”
Coun Martin, who was speaking at a recent meeting of the town’s youth council, added a new supermarket would be welcomed by many town residents,.
However, she said it would have to be in ‘the right place’ with good access.
Coun Angela Birchall, also speaking at the youth council meeting, said she was concerned a retail development on the site could cause traffic delays in the town centre.
Representatives from Queen Elizabeth’s Grammar School - also sited on West Street - said they were also worried about the impact a major development would have.
One QEGS student told the meeting the amount of traffic on West Street was a concern, particularly at the start and finish of the school day.
He added he was ‘surprised’ there had not been a major accident on West Street.
Town councillors have been campaigning for improvements to West Street for several months.
They say that parked vehicles can lead to access issues for emergency vehicles and buses.
However, Coun Alan Lockwood has warned that removing or restricting parking could have an impact on residents who don’t have any alternative to leaving vehicles outside their properties.