Ofcom said in a statement that it had a duty to ensure that broadcast licensees are "fit and proper" to hold their licences.
"We have today written to ANO TV Novosti, holder of RT's UK broadcast licences, which is financed from the budget of the Russian Federation," Ofcom said.
"This letter explained that, should the UK investigating authorities determine that there was an unlawful use of force by the Russian state against the UK, we would consider this relevant to our ongoing duty to be satisfied that RT is fit and proper."
Russia Today, now known by its acronym as RT, was set up in the mid-2000s to counter what Russian President Vladimir Putin saw as the dominance of American and British international media organisations and their allegedly pro-Western bias.
More From This Section
The channel is seen by its critics as giving a platform to conspiracy theorists as well as far-right or anti-establishment figures who emphasise Western hypocrisy or corruption.
Several lawmakers called for a ban on RT on Monday after Prime Minister Theresa May said it was "highly likely" that Russia was behind the attack on March 4 on former double agent Sergei Skripal.
"It is a propaganda mouthpiece for the Russian state and should not be engaged with by any democratic politicians," Wilson said.
May said MPs should be "very wary and very careful" in appearing on RT and said the issue was "obviously... of concern".
The channel responded scathingly on Tuesday, saying: "It is regrettable to see RT so quickly proposed to be sacrificed as a political pawn".
The channel said such a restriction would be equivalent to "doing away with any concept of press freedom in the UK," adding that it played a vital role in "completing the picture of news".