On Wednesday night Federation Internationale de Football Association were asked to offer their view on the political situation between the World Cup hosts and one of the nations participating in their tournament, but remained confident that England would travel to Russia this summer.
The Russian channel announced Mourinho as its main pundit for Russia 2018 a day after the incident in Salisbury, but the Manchester United manager has repeatedly refused to answer any questions about the role.
The announcement came in the wake of the attempted murder of Russian former spy Sergei Skripal and his daughter, Yulia, by use of a nerve agent in Salisbury.
British politicians have appeared on RT, where former Scottish First Minister Alex Salmond hosts a talk show.
Bryant's message was echoed by fellow Welsh Labour MP Stephen Doughty.
The provocation by western countries, based on the alleged poisoning of a former Russian official and the accusation against Moscow for that action, aims to sabotage the FIFA World Cup in this country, the Foreign Ministry denounced today.
Broadcasting regulator Ofcom issued a statement on Tuesday, following Prime Minister Theresa May's update on the investigation to parliament on Monday, and said it would wait for her next public comments on Wednesday before considering "the implications for RT's broadcast licences".
But a boycott is considered highly unlikely as it would put the FA on a collision course with global football governing body FIFA, whose regulations insist member national authorities must run the sport in their respective countries without "outside interference" from the government or any other parties.
There may also be retaliation against British journalists if broadcast regulator Ofcom decides to revoke the United Kingdom licence of Russia Today, the Kremlin-funded channel accused of pumping out propaganda and fake news.
A FIFA spokesperson said: 'FIFA and the local organising committee have full confidence that all 32 participating teams and football fans from around the world will make this another memorable World Cup.
"This letter explained that, should the United Kingdom investigating authorities determine that there was an unlawful use of force by the Russian state against the United Kingdom, we would consider this relevant to our ongoing duty to be satisfied that RT is fit and proper".