The broadcaster is a known friend of Pietersen and last week waded into the debate after the 33-year-old was released from his central contract by the ECB in the wake of the horror Ashes tour.
No real reason was given for Pietersen's removal from the national team at the time, with Morgan laying into former team director Andy Flower, Cook and wicketkeeper Matt Prior for what he believed were their roles in his friend's departure.
Morgan went on to tweet what he believed was an account of what Prior had said in a team meeting during the Melbourne Test against Australia, amid a flurry of allegations that Pietersen had been stabbed in the back by his colleagues.
Speculation surrounding Pietersen has continued, with the ECB moving to try and end it with a statement on Sunday, the headline of which was Cook needed to "have the full support of all players, with everyone pulling in the same direction and able to trust each other".
That appeared to suggest Pietersen was not to be trusted, and the statement went on to reference allegations made by people "outside cricket", which Morgan has taken to mean himself.
"Is this @ECB_cricket statement the most absurd ever made by an English sporting body? Serious question," he tweeted.
Cook was present at the meeting in which Pietersen was told he was no longer needed, and Morgan added:
"After the way he betrayed @KP24 - I wouldn't trust Alastair Cook to take my dog for a walk. And I don't even have a dog. #Judas."
The statement did not suggest that Pietersen had been stood down because of Morgan's comments, but that did not stop him from adding:
"As for 'trust', which England players grassed up @KP24 to (Andy) Flower from that 'confidential' meeting? What shameless hypocrites."
Morgan went on to try to debate with BBC commentator Jonathan Agnew:
"Erm @Aggerscricket - it was Flower, Cook & Prior who stabbed KP in the back for no good reason. You need better sources".
"Again @Aggerscricket - how could the ECB sack KP for revelations leaked AFTER he was sacked. Please explain.
The statement from the ECB had been met with surprise in some quarters and Morgan led the derision.
"I may be 'outside cricket' @ECB_cricket - but I've also helped pay your wages for over 30 years as an England cricket fan."
Despite there being no comment from Pietersen's management, Morgan claimed to have spoken to the 33-year-old, saying the word "trust" had never been used.
Just spoke to @KP24 - nobody has EVER raised the issue of 'trust' with him between rehabilitation & sacking. Not ECB, Cook, anyone. Fact.
"ECB not produced a single shred of evidence that @KP24 breached Cook's, or anyone else in team's trust since coming back into side. Fact.
"So, when it comes to @ECB_cricket & Alastair Cook claims that @KP24 breached their 'trust' - don't 'trust' them. #BringBackKP"
Morgan went on to claim some of Pietersen's team-mates had been complicit in things appearing in the media, adding:
"Given half the England team have leaked derogatory stuff about @KP24 to the papers, will they all now be sacked too? #DoubleStandard."
- Sports & Recreation