The former Liberal Democrat leader is speaking out following the ongoing controversy over the poisoning of former Russian agent Sergei Skripal and his daughter.
Jose Mourinho's decision to work as a World Cup pundit for Kremlin-backed television channel RT has been strongly criticised by MPs following the Salisbury poisoning attack.
Chris Bryant, an opposition Labour MP for the Welsh constituency of Rhondda, told Britain's Press Association news agency on Tuesday: "To my mind, this is blood money, paid directly from the Russian state coffers".
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.
Former Scottish National Party leader Salmond faced similar criticism when he became a presenter for RT previous year. British Prime Minister Theresa May said on Monday that it was "highly likely" that Russian Federation was behind the attack and promised "extensive measures" against the country if an explanation was not provided.
When British foreign secretary Boris Johnson first raised the notion of England boycotting this summer's World Cup in protest at what has been dubbed spy-gate, he was roundly condemned and his office was quick to issue a clarification saying he meant officials and politicians rather than the team itself. "I would urge leading football figures to rethink - not least after this week's revelations - whether their punditry on Putin's mouthpiece is appropriate".
'Can our national football team play in the World Cup in Russian Federation with a clear conscience when this is going on?'
The FA is adamant that worldwide relations with Russian Federation are none of its business, and will leave those political considerations to Government.
It follows calls from MPs for the organisation's United Kingdom broadcasting licence to be withdrawn.
Bryant's statement came as Mourinho was busy with United's Champions League last-16 second leg against Sevilla at Old Trafford tonight.