Coun Jade Morgan, who has put the motion forward, argued that with such protections in place, more women would be encouraged to stand to be councillors.
She is bringing the proposals to a meeting of full council at Preston Town Hall on Thursday, December 19.
“We don’t actually have a parental leave policy at the moment,” she said.
“I think it is actually one of the things that is keeping away family members.
“For members who want to start a family in the future, it’s a big duty to be on the council.
“It takes up a lot of time.
“We have had councillors who have said they would have to leave the council because they wanted to start a family.
“We shouldn’t have to make the choice.
“It would be in line with national policy.
“It harks back to the time when it was men who ran the country and they didn’t have to worry because their wives would be at home raising the family.
“I think it’s quite an uncomfortable conversation.
“Hopefully, it will encourage women into the council if we have these protections in place.”
The motion, which suggests taking on the policy drafted by the Local Government Association (LGA), states: “Introducing a parental leave policy is a step towards encouraging a wider range of people to become councillors.
“It also encourages existing councillors who may want to start a family to remain as councillors.”