Monmouthshire, Rhondda Cynon Taf, Merthyr Tydfil and Vale of Glamorgan councils say they are considering the move to stop “irresponsible lending”.
Instead they would promote other ways of accessing financial help.
The Consumer Finance Association said it feared people could be stopped from accessing responsible credit providers.
About two million people in the UK use payday loans, which are designed as short-term access to cash, with relatively high interest rates, until the applicant is next paid.
Some councils in England, including Plymouth and Leeds, have already banned access to their websites from council computer terminals.
The Labour group in Monmouthshire wants its local authority to do the same, saying it would help vulnerable people who may feel they have nowhere else to turn for money.
It has put forward a motion to block access to the websites for both members of the public and staff from council-run libraries, buildings and wi-fi spots.
Councillor Dimitri Batrouni, leader of the Labour group in the county, said he believed there was cross-party support for the idea, which the full council will vote on on Thursday.
“I have heard anecdotal evidence of people taking out a loan but because of the huge interest rates they are unable to pay it back,” he said.
“It’s a vicious circle of debt for people who are struggling.
“We want to see access to the websites blocked to try to stop irresponsible lending. But obviously if people want to access them, they’ll do it elsewhere.
“So it’s more about the council sending out a message that there are alternatives out there and that people can ask for help from places like the Citizens Advice Bureau and credit unions.”
Rhondda Cynon Taf council said that a report recommending banning access to payday loan websites would be considered “shortly”.
It said that computer users would instead be pointed to the support offered by credit unions.
The Vale of Glamorgan and Merthyr Tydfil councils also said it was also considering the move, although no decision has yet been taken.
Other councils contacted by BBC Wales said they were not looking into banning the websites but instead were keen to promote financial management advice.
John Killion, chairman of the North Wales Credit Union – a financial co-operative owned by the people that uses it – said he would welcome councils restricting access to payday loan websites.
“We’re convinced that the way the payday lenders are lending is quite irresponsible,” he said.
“They’re not looking at people’ ability to repay.
“I was talking to the manager of our Rhyl office who gave the example of someone who had taken out five payday loans while receiving benefits.
“They had got themselves into such a state and came to us for help. However, it was too risky for us to lend them money.”
“I think councils have a responsibility to look at the health of their communities and one of the things that makes them unhealthy is financial exclusion.
“People see the slick adverts of these payday loans companies and think they are the only and easy options. But they are not and people just get in deeper and deeper.”
However, Russell Hamblin-Boone, chief executive of the Consumer Finance Association which represents some of the largest and most responsible payday lenders in the UK, said it was concerned about the possible restrictions.
He said that while the association would support any initiatives that drive out irresponsible lenders, it feared a ban would prevent people having access to responsible credit providers.
“Responsible lenders explain the costs up front in pounds in pence; use credit reference agencies to check your details and will not lend to you if they think it will make your financial situation worse,” he said.
“YouGov research released earlier this month shows that these measures are benefiting payday borrowers in Wales with 95% of those surveyed saying they fully understood the cost of their loan.”