The website Cyberscoop cited two officials said to be familiar with the matter in a report that claimed Treasury Secretary Steve Mnuchin had approved the additional sanctions but many of his advisers were opposed.
The move to impose additional sanctions has been largely driven by the US National Security Council and could lead to a ban on Kaspersky operating in the US.
The US has already announced two rounds of sanctions against Russia. The second, made public on 7 April, included measures against seven high-profile Russian businessmen, a dozen of their companies and 17 senior government officials.
The report said some US Government officials were afraid that imposing more sanctions on Kaspersky might well lead to tit-for-tat action by other countries some day.
One person who was said to be familiar with the sanctions plan was quoted as as saying: "After all, what’s stopping China from punishing Apple if they found out they were conforming to a National Security Letter or something?" Such letters are used as subpoenas to compel private companies to give evidence.
"You know, that’s the sort of question that needs to be asked. How would this affect that calculus for others in the future, right? I don’t know," the unnamed person added.
Another source said: "Sanctions would be a bullet in the head for Kaspersky. It would kill their business not just here but pretty much anywhere that enjoys the benefits of using the US banking system. This could have a reverberating impact that comes back to hurt us … sometimes these things have unintended consequences.”
Kaspersky has a couple of lawsuits in progress against a ban imposed on use of its products in the public sector last year. The company has come under heightened suspicion of colluding with Russian intelligence following the US presidential elections in 2016.
The US Department of Homeland Security banned the use of the company's products in the public sector on 13 September 2017. 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 2017, 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 programs, while Israeli intelligence officials looked on.
In other actions against Kaspersky Lab in the US, its products were taken off the shelves by retailers Best Buy and Office Depot. And recently, it was revealed that Twitter had imposed an advertising ban on the company.