The state-backed outlet announced the appointment of the Manchester United manager as their main pundit for Russia 2018 a day after the Salisbury poisoning attack involving a former Russian spy and his daughter.
Mourinho has refused to answer questions on his involvement with the channel - formerly known as Russia Today - since the incident.
In a statement given to PA, Rhondda MP Bryant said: "To my mind, this is blood money, paid directly from the Russian state coffers."
Bryant, a Labour MP who in 2015 briefly served as shadow secretary of state for digital, culture, media and sport, has previously called for RT's "propaganda" to be banned in the UK.
Prime minister Theresa May claimed that it is "highly likely" Russia was responsible for the Salisbury incident, while Russia's foreign minister Sergei Lavrov has described claims of state involvement as "rubbish".