The Leader of the Commons has stepped in after it emerged council chiefs were considering awarding contracts to provide transport for children with special educational needs (SEND) to two firms run by Azeem Hafeez, a former employee at the authority.
Sandwell Council announced on Wednesday it had delayed a decision to ensure that "proper process had been followed".
Companies run by Mr Hafeez – North Birmingham Travel and County Cars – were the only firms successful in a closed bid tender process.
He was previously named in the Wragge Report probe into suspect land deals along with his father, former council deputy leader Mahboob Hussain.
Speaking in the Commons, Mr Rees-Mogg said he would be raising the "extremely troubling" concerns with Home Secretary Priti Patel and Local Government Secretary Robert Jenrick.
He said the situation at the council was already being monitored "closely" by the Ministry of Housing, Communities and Local Government, and added: “But it may also be something that the police ought to be looking in to.
"This sounds like a really serious prima facie case."
Mr Rees-Mogg was responding to a statement from West Bromwich East MP Nicola Richards, who has called for an urgent parliamentary debate on the matter.
She told MPs: "Both of these companies are owned by the same person, a former council employee and the son of a former Labour deputy leader of Sandwell Council, named in the damning Wragge Report, where both father and son were revealed to have been involved in land deals."
Ms Richards later said: "Questions need to be asked as to who was involved to progress this to such an advanced stage.
"It’s clearly a result of a deeply flawed procurement process, which shows its business as usual at Sandwell Council, despite vague promises of a culture change from as high up as the Leader of the Labour Party.
“It comes as no surprise to me that these historic issues run deep, and whilst I can’t say I am shocked, I am saddened it appears that still no lessons have been learnt."
She added: “It’s about time a real culture change happened in Sandwell Council, so that the local authority works to improve the lives of its residents, and not friends and family of those in senior positions.
“If the only way to bring these issues to the attention of the relevant authorities is to raise it on the floor of the House of Commons, then so be it."
Mr Hussain and Mr Hafeez were at the centre of the 2016 Wragge Report, which alleged code of conduct breaches by Mr Hussain.
Mr Hafeez was arrested during the scandal before being released without charge and the investigation was dropped. Both he and his father have denied any wrongdoing.
Speaking at a council cabinet meeting on Wednesday, Sandwell Council leader Rajbir Singh, said he was "aware of a number of concerns being raised" over the contracts.
"I think it's appropriate we first satisfy ourselves the proper process has been followed before any decision is made on this matter," he added.