A report in Britain's Financial Times said a senior Whitehall official had said that the intelligence and security organisation GCHQ had expressed concerns about Kaspersky software for many months.
It said that the GCHQ feared that Kaspersky may have been taken advantage of by the FSB, the successor to Russia's KGB, and used for snooping on foreign targets.
Kaspersky Lab has come under heightened suspicion of colluding with Russian intelligence following the US presidential elections in 2016.
Reports in mainstream US media have ramped up the pressure on Kaspersky which has since closed down its office in Washington DC.
During the first half of October, the three big US mainstream newspapers made serious allegations about the company.
A report in The Wall Street Journal on 11 October hinted that Kaspersky Lab could have made available its source code to the Russian Government.
Prior to that, a report in the Washington Post on 10 October claimed that Israeli Government information security professionals had found NSA hacking tools in Kaspersky Lab's system when it gained access to the company's servers in 2014.
And The New York Times claimed on 11 October that Russian Government employees had used Kaspersky's anti-virus software to search for the code names of US intelligence programmes, while Israeli intelligence officials looked on.
Contacted for comment, Kaspersky Lab responded: "The Financial Times article points out that 'No evidence suggests that any data of Barclays customers have been compromised by use of Kaspersky software on their computers'.
"Also, Barclays’ representatives confirm in the article that the British authorities and regulators have not addressed the bank in regards to its partnership with Kaspersky Lab.
"All the allegations against Kaspersky Lab in the article are based only on the information from anonymous sources that does not contain any credible facts.
"The only goal of our products and services is to protect users from cyber threats. Kaspersky Lab has never helped, nor will help, any government in the world, including Russia, with its cyber espionage or offensive cyber efforts. In addition, more than 85% of its revenue comes from outside Russia, which further demonstrates that working inappropriately with any government would be detrimental to the company’s bottom line."
Adam Maskatiya, general manager, UK & Ireland at Kaspersky Lab, said: "Kaspersky Lab continues to work with Barclays to provide its customers with Internet security. Barclays, through its global reach, has done much to improve public awareness of cyber security threats and we look forward to continuing our relationship to help keep its customers protected on-line."