The return of Dáil sittings at Leinster House on Tuesdays and Thursdays is being proposed by the Deputy Government Chief Whip.
Fine Gael's Brendan Griffin has asked the Ceann Comhairle to consider his proposal to have the majority of Dáil sittings taking place in Leinster House again.
The Dáil has met in the Convention Centre Dublin since the middle of last year.
Recently the Ceann Comhairle Seán Ó Fearghaíl said that politicians had taken this decision reluctantly but were bound to follow public health advice.
However, Deputy Government Chief Whip Brendan Griffin believes that two-hour Dáil speaking sessions followed by 15 minutes breaks for cleaning and ventilation could pave the way for a return to Kildare Street.
He said the numbers required for votes on these days could be reduced to possibly 21 from the current 45, while the number of TDs in the Dáil Chamber at any one time would also be capped.
The full weekly votes would still take place at the Convention Centre every Wednesday, under this plan.
The proposal comes as Tánaiste Leo Varadkar has again stated that he is seeking to progress a plan to allow employees return to the workplace in August.
The matter was discussed at the Covid-19 Cabinet Committee meeting on 27 May, which was attended by Chief Medical Officer Dr Tony Holohan.
Speaking the following day, Mr Varadkar said the Government was looking at a staggered return of employees to the workplace in August.
Government believe this would allow time to have large numbers of people back in their offices in advance of the busier period in September when schools and colleges return.