The Green party and Fianna Fáil have both launched bills on a directly-elected mayors.
The Fianna Fáil bill applies solely to the capital while the Green Party would like it extended to other cities.
Fianna Fáil's bill will be debated during Private Members' business this evening in the Dáil.
They suggest the election would be held in conjunction with the local elctions in 2019. The party wants to consult further on the matter.
The Green Party is looking for mayoral elections in cities across the country and say this would not result in additional expense.
It is the same bill that they sought to introduce while in government with Fianna Fáil.
The Green Party is also bringing forward a bill in the Seanad to end the manufacture and sale of plastic microbeads in cosmetic products.
Party leader Eamon Ryan said they had all-party support although Fianna Fáil may want to bring its own bill on the matter.