At a full council meeting on Monday Labour group leader Aftab Nawaz is set to officially propose Councillor Sean Coughlan for the position of deputy mayor, which has been vacant since the death of Councillor Harbans Sarohi in July.
But the ruling Conservative group says it plans to vote down the move.
In a letter to Councillor Nawaz, Walsall Council leader Mike Bird said the Tories will vote against the proposal and urged his opposite number to put forward another candidate.
Mr Bird said Mr Coughlan, a former council leader, had previously spoken of how the "pressures of public life" had led to him suffering mental health issues. He had also accused members of the Conservative group of being the cause of his problems, the letter added.
Mr Bird said: "Not being in possession of any substantive evidence of Councillor Coughlan’s mental health condition during his six months of absence, or indeed the current position of his health, my members do not wish to be in a position where Councillor Coughlan once more could blame the Conservative group for any deterioration in his health, if they were to be the architects of his appointment to the position of deputy mayor with onward transmission to the position of Mayor in 2022/2023."
In 2019 Mr Coughlan revealed how the pressures of running the borough's Labour group had contributed to him attempting to take his own life.
He told the Express & Star he was in a "much better position" than he had been for many years.
"The period where I have been recovering from mental health issues I have used to support people who are going through the same problems," he said.
"I believe the opportunity of being deputy mayor this year and mayor next year would show people that no matter how tough things get, with the right support there is some light at the end of the tunnel."
Mr Coughlan said he was "disappointed" that the Conservatives appeared to be suggesting he had lied about mental health issues, and said he had spoken about the subject freely "because I want to try and help people".
He added: "To vote against me is saying to anyone, that if you have mental health problems and it is work related, even if you manage to overcome it and return, you should never ever have an opportunity to progress.
"That's a really sad message to give to people."