Winnipeg Mayor Brian Bowman says after RCMP conclude their investigation into the construction of the new police headquarters, the city might ask the province to conduct a public inquiry.

Bowman told reporters on Tuesday that he is "deeply troubled" by "serious allegations" contained in an RCMP application for a search warrant.

The RCMP search warrant application alleges former mayor Sam Katz received 10 to 12 personal cheques from Caspian Construction, the contractor at the centre of an investigation into the construction of the city's new police headquarters.

Katz told CBC the cheques were for Jets tickets or concert tickets.

When asked whether it's appropriate for a sitting mayor to sell tickets to sold-out events at the MTS Centre, including Jets games, Mayor Bowman refused to answer.

"I'll let Sam Katz speak for Sam Katz," Bowman said.

Fraud and forgery allegations were also made in court documents tied to the case, including allegations that invoices were said to be "improperly associated to the WPS building when in fact the work was either done at other city properties, private properties or was not done at all."

None of the allegations have been proven in court.

The original cost of the new police headquarters was estimated to be $135 million but it has run millions over budget.