Fianna Fáil, Fine Gael and Green Party MEPs want the rule lifted if they test negative for Covid before leaving Brussels.
It comes after the resignation of Commissioner Phil Hogan who didn't restrict his movements when he travelled home.
A decision on his replacement is expected today or tomorrow - with two candidates, a man and woman, due to be put forward.
Euronews political editor Darren McCaffrey says the Commission is becoming frustrated at how long it's taking:
