Labor is preparing to do a deal with the Greens on asylum-seeker medical transfers after the minor party raised concerns about proposed amendments.

The opposition and crossbench MPs are locked in discussions about making it easier for sick asylum seekers to be flown to Australia for treatment.

The fragile alliance wants doctors, rather than politicians, to be the arbiters on medical transfers, and a bill is due to be voted on in parliament on Tuesday.

Labor suggested changes to the proposed laws, taking out a definitive timeline for medical transfers and allowing the Home Affairs minister to reject transfers on character grounds.

But after the Greens said there would be no deal if that was the case, the two parties are close to an agreement.

Labor has agreed to a definitive time frame for medical transfers and the character test will be limited to avoid people being rejected for crimes Australia doesn't recognise, such as being gay.

There will also be a pathway for appeals through the Administrative Appeals Tribunal.

A Labor spokesman would not confirm whether a deal had been struck, but said negotiations would continue until Labor's amendments to the proposed bill were officially circulated before the vote on Tuesday afternoon.

The coalition government is opposed to any changes to border protection bills, arguing the minister will lose the discretion over who is transferred to Australia.

The government no longer has enough numbers in the lower house to avoid a defeat on the bill.