Mr Meredith was arrested on Friday and bailed by police until June
The government could step in at Stoke-on-Trent City Council as the elected mayor fights corruption allegations.
The Department of Communities and Local Government (CLG) may act after Mark Meredith stepped down from some duties.
A spokeswoman said the department was "ready to play our part" and was monitoring the situation closely.
Mr Meredith was arrested on suspicion of misconduct in a public office and complicity in corruption while in public office. He denies the claims.
He was released on police bail until June, following Friday's arrest.
It is thought police have been looking at council proposals for a leisure centre.
The CLG spokeswoman said the situation was "entirely a matter for the council and the legal authorities concerned".
She added: "We are monitoring the situation closely and stand ready to play our part to enable the people of Stoke to have the effective and accountable council which they deserve."
Mark Fisher, Labour MP for Stoke-on-Trent Central, said government intervention remained "the position of last resort".
Mr Meredith, 43, denies the allegations made against him, and says the claims were "politically motivated".
He will stay in his constitutional role as elected mayor of the city but has stood down as chair of the executive and members' board.
The authority's deputy mayor Mohammed Pervez will take over the duties.
Stoke city councillor Roger Ibbs, leader of the Conservative and Independent Alliance and the portfolio holder for education, was arrested last month as part of the same inquiry.
Mr Ibbs said he was arrested following a complaint he made to the council.