According to reports, Sajid Javid will back the end of passenger locator forms by Easter.
The Guardian reported that Javid had been pressured by Shapps ahead of the meeting.
The PLF will be removed in time for the Easter holidays, marking an end to restrictions introduced as a result of the Covid pandemic.
Sources said the Department of Health, the chief medical officers and the Scottish government were against its removal.
Robert Courts told the Airlines UK annual dinner in London this week that they have heard your concerns in the passenger locator form. The secretary of state and I both want the PLF gone as soon as possible.
We have had one of the most open Covid regimes in the world. The government is Conservative. We will not become addicted to bureaucratic restrictions.