By Amanda Ferguson

BELFAST (Reuters) - Northern Ireland could have a different relationship to the European Union's single market or customs union from the rest of the United Kingdom following its exit from the EU, the leader of the British province said on Saturday.

The head of Scotland's devolved government Nicola Sturgeon this week said she would make specific proposals over the next few weeks to keep Scotland in the single market even if the rest of the UK left, and that British Prime Minister Theresa May had said she was prepared to listen to options.

Northern Ireland is the only part of the United Kingdom with a land border with the European Union and First Minister Arlene Foster has repeatedly said she wants to avoid a "hard border" with border posts and customs checks with the Republic of Ireland.

Asked by Reuters if Northern Ireland might have a special status in relation to either the customs union or the EU's single market Foster said "those are all matters, of course, for negotiation."

"Because of our history and our geography that things will be slightly different here in Northern Ireland," said Foster, speaking on the sidelines of her party's annual conference.

"We have to recognize that we are the only part of the kingdom with a land border with the European Union so all of those issues have to be sorted through in the negotiation."

She declined to give any further details of how a settlement might look.

The EU has said Britain's exporters can have access to its single, tariff-free market of 500 million consumers only if it maintains the freedom of movement of people with the rest of the EU, which many supporters of Brexit oppose.

Remaining part of the customs union would allow Britain to trade freely with the bloc but would require it to share its common external tariffs, which could complicate attempts to strike free trade deals with other countries.

Fifty-six percent of Northern Ireland voters rejected Brexit at the referendum in June. But Foster, who campaigned for Britain to leave said those opposed to Brexit should accept the will of the 52 percent of Britons who voted to leave.

Foster has mocked the "remoaners" who refuse to accept the vote and welcomed the rejection by a court on Friday of a legal challenge to Britain's moves to exit the union.

"All of this niceties around who voted what way is over. The vote has been had. We now need to get on and make it a success for everyone and that includes those people who didn't want to leave."

"I have no time for those who want to refight the referendum," she said.

Foster said she had good relations with the government of the Republic of Ireland, but criticized it for attempting to use Brexit to poach foreign direct investment jobs from Northern Ireland.

"It has been told to me from a number of sources that their representatives, particularly in the United States of America are visiting companies that either are in Northern Ireland or are thinking about coming to Northern Ireland,"

"I think it is wrong for them to say one thing publicly in relation to the island of Ireland and then to run around trying to steal our inward investors on the other hand."

(Editing by Conor Humphries and Richard Balmforth)