McGovern said that the BBC's compliance unit asked for scenes from the BBC One drama to be removed as they could cause potential offence to fans of the football club.
Speaking to The Radio Times, the Cracker creator said: "I ask, 'What is the point of this unit?' And the response is, 'It's in case you cause offence'.
"They've asked questions, particularly about the anti-Manchester United bias in The Street. There was this big spiel about a character wanting to shoot Wayne Rooney and Rio Ferdinand. I told them every chance I get I write with anti-Manchester United bias."
The Liverpool-born writer added: "I'm a dramatist. Imagine on my tombstone if it read, 'Jimmy McGovern, writer - never offended anybody'. How would I feel? That's my job."
The BBC Trust ordered the corporation to tighten up its compliance procedures after The Queen was misrepresented in a 2007 promotional trailer. Additional measures were brought in after the Manuelgate scandal in 2008, when Jonathan Ross and Russell Brand left lewd messages on the answering machine of actor Andrew Sachs.
However, a BBC spokesman disputed that McGovern had ever been told he "can't write with an anti-Manchester United bias".
He said: "In fact, no-one at the BBC has ever told Jimmy what he can and cannot write at all. Occasionally people will ask questions about why he has chosen a particular theme or subject, but that's all."
McGovern's latest project for the BBC is Accused, a series of six hour-long dramas about ordinary people who find themselves in front of a judge.
Despite his comments about the BBC's compliance procedures, McGovern admitted that the corporation largely respects his creative freedom.
"I don't think anyone [at the BBC] has ever come back to us about a story. We ask questions ourselves - and the question we ask is, 'Is this real?'" he said.
"There are no black people in my dramas, or very, very few, but that's because I understand the white working class and I write about that.
"I don't think that's ever been put to us by the BBC. We did three series of The Street and the three of them were good. So I think the BBC respect us."
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