THE Bayswater City Residents Association wants a public vote for mayor rather than a council vote.
President Tony Green said its members believed a public vote would bring more democracy to council.
Cr Bull has confirmed he will put his hand up for the mayoral position, while Cr McLennan will consider contesting for Mayor, if she is re-elected.
Both were voted by fellow councillors to the position for the first time in 2017.
Current Bayswater Deputy Mayor Chris Cornish and Bassendean Deputy Mayor Bob Brown will not be re-contesting their seats.
The two councils and the City of Gosnells are among a few in Perth that still allow councillors to vote for their mayor.
The City of Stirling is holding its first public vote this year.
Cr McLennan said she saw advantages and disadvantages of both methods.
“As the mayor is the leader of the council and the conduit between elected members and the administration, it is imperative that they have a good working relationship with fellow councillors,” she said.
“I’ve come to appreciate that a significant benefit of a council-elected mayor is that the individual who takes on this role has the support of at least the majority of councillors.
“In the situation where the community elects the Mayor there is the possibility that the successful candidate may not always have the support of their fellow councillors, potentially making the dynamics more challenging.”
Cr Bull said he supported in-principle a mayor being elected publicly.
“I also believe that consideration needs to be given to how easy or difficult it would be for a local to seek mayoral office,” he said.
“The larger the district, the more expensive and sophisticated the campaign so we wouldn’t want a situation where locals are effectively locked out of the chance to be mayor because of a lack of money or experience in campaigning.
“Whether or not the City of Bayswater is the right size district or too big, is a question to be considered.”