Elected mayors are allowed to introduce a levy, which households pay automatically alongside their council tax, to help fund public spending.
Ms Brabin's office has inherited the precept previously set by the Police and Crime Commissioner for West Yorkshire, whose role was merged with hers upon her election victory last month.
That money is used to help fund local policing, but she would be entitled to introduce a further levy to top up cash handed down from the government.
But Tom Gordon, the leader of Wakefield's Lib Dem group, will put forward a motion at a meeting on Wednesday, suggesting Wakefield Council write to Ms Brabin and requests she rule out an extra levy.
Speaking ahead of the meeting, Coun Gordon said: "A West Yorkshire mayor was something that the people of Wakefield didn't want in the first place.
"More people were strongly opposed than in favour of it.
"The turnout for the consultation the council held on it was abysmal, but despite that the Labour administration took us into a new combined authority.
"What I heard on the doorstep was that people don't want to pay for this.
"I've put this motion forward for people who are really concerned about their finances and can't afford the burden of having to pay an extra precept."
While some mayors across the country have imposed an extra precept, others such as South Yorkshire metro mayor Dan Jarvis and Ben Houchen in the Tees Valley, have not.
The West Yorkshire Combined Authority (WYCA) has been contacted for comment.
Local Democracy Reporting Service