There is also anger that Greece has been slow to let in EU experts and improve its registration of refugees.
The influx of migrants across countries with few border restrictions has alarmed European leaders and raised doubts about the very future of the 1985 Schengen accord.
Now, according to the FT, Greece has been repeatedly warned this week that it could be suspended from the 26-member zone if it fails to take action before an EU leaders` summit in mid-December.
Separately, unnamed officials in Brussels have said that a suspension has been discussed in recent days in an attempt to persuade the Athens government to improve its handling of migrants and refugees.
Greece is not only struggling to cope with the numbers of people arriving on the islands closest to Turkey such as Lesbos, but thousands of people are camped on the northern border with Macedonia, which has erected a fence to stop people crossing.
Greece`s EU partners are frustrated that the Athens government has been slow to accept offers of help from the border agency, Frontex, to better manage its sea border. The offer is particularly sensitive in Greece because of concerns over its national sovereignty.
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