Tasmanian senator Jacqui Lambie has asked the Morrison government to revive the option of sending offshore asylum seekers to New Zealand as it courts her critical vote in attempts to scrap the controversial "medevac" laws.

The influential crossbencher said on Wednesday she had put forward one condition in which she would support the federal government to repeal legislation which allows for the transfer of asylum seekers on Manus Island or Nauru to Australia for medical treatment, but would not reveal her ultimatum on national security grounds.

Senator Jacqui Lambie says she will repeal the Medevac Bill on one condition. Credit:Alex Ellinghausen

Multiple sources with knowledge of Senator Lambie's negotiations with the government have told The Age and The Sydney Morning Herald she had canvassed a potential third-country resettlement deal to move "as many" asylum seekers off Papua New Guinea and Nauru as possible during her discussions.

Senator Lambie said the condition she had put to the government was a "sensible and reasonable" proposition which she had arrived at through "extensive consultation".