"The negotiations are continuing on what a workable backstop looks like - those negotiations haven't concluded", the spokeswoman said.
However she stressed the United Kingdom would be operating its own "independent trade policy" after the end of 2020 when the planned 21-month transition period expires.
In talks with European Commission President Jean-Claude Juncker and European Council President Donald Tusk, she reiterated her view that a backstop agreement put forward by Brussels to prevent a hard border was unacceptable.
Mrs May said Britain would have an "independent trade policy" after its departure but Ireland has proposed a "backstop" if no new customs arrangements are finalised before the end of the transition period, the Telegraph reports.
The Irish premier has warned Britain that it must keep some ties to the single market with Brexit in order to avoid a hard border with the Republic.
Britain also wants to be able to forge its own trade deals with non-EU countries.
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Varadkar said: "If we're not making real, substantial progress by June then we seriously need to question whether we're going to have a withdrawal agreement at all". "It would certainly help us continue to trade between Britain and Ireland much as we do now".
Her promise to bring forward her alternative plan came as Irish Taoiseach Leo Varadkar warned Britain's European Union withdrawal agreement could be in jeopardy unless the deadlock was resolved.
Under such a scenario, Britain would not be given the adaptation period from next March to the end of 2020, but go straight out of the European Union with little detail agreed on how to handle its ties with the bloc.
Mrs May acknowledged the concerns of the Irish Government would have to be dealt with so "we do not have a hard border between Northern Ireland and Ireland".
The British Ports Association - whose members include ro/ro ports handling over half of all UK-EU trade - is in favor of retaining the benefits of the EU Customs Union in some form.
Meanwhile, the government has indicated that it will attempt to overturn a raft of Lords amendments to its flagship EU (Withdrawal) Bill next month.