Mr Wright has faced calls to step down after a report on child abuse in Rotherham, where he managed children's services between 2005 and 2010.
The report said at least 1,400 children were sexually exploited from 1997-2013, mainly by gangs of Pakistani heritage.
A Labour MP now wants a possible misconduct case against Mr Wright.
'Tip of iceberg'
The report also revealed there had been three previous inquiries, including one written in 2006 during Mr Wright's tenure in children's services, which provided "stark evidence" of the situation in Rotherham.
Meanwhile, the former director of children's services in Rotherham, Sonia Sharp, said she was briefed by politicians, senior managers and frontline staff about the issue of sexual exploitation of young people when she took up her post in 2005. She left Rotherham Council in 2008.
Dr Sharp said it was already known when she joined there were "many children in the community at risk" and staff feared "this was the tip of an iceberg".
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Home Secretary Theresa May says Shaun Wright should "heed calls" to resign
Local Government Secretary Eric Pickles attacked poor scrutiny in local government.
He said: "It is appalling that institutionalised political correctness led to the council turning a blind eye to heinous crimes.
"Britons across class, colour and creed will be appalled at the criminal acts that were committed and the failure of municipal governance.
"The biggest enemy to good community relations is failing to confront and challenge those who do wrong.
"This is a wake up call for local government - from the inadequate scrutiny by councillors of protection for the vulnerable to the conspiracy to cover up uncomfortable truths to avoid awkward questions, and the subsequent failure to sack those guilty of gross misconduct.