Meanwhile, Leo Varadkar, the Irish prime minister, expressed a similar sentiment as he said he is "very hopeful" of a deal being done this week.
May is expected to commit to restoring power-sharing, and reaffirm the principles of the Good Friday agreement which underpins the devolved system of government at Stormont.
Sinn Fein has argued that Brexit could undermine the agreement if it leads to any border checks between Northern Ireland, which will leave the European Union with the rest of the United Kingdom in March 2019, and the Republic of Ireland, which will remain an European Union member.
The previous local administration collapsed in January 2017 with the resignation of its Sinn Fein Deputy First Minister Martin McGuinness over a botched energy saving deal.
She said: "I am hopeful that we will move toward devolution again. It is about finding an accommodation that recognises the need to respect all languages and all cultures in Northern Ireland and not allow one to dominate over another".
She later added: "There isn't a deal yet but there is very good progress and we will keep at it and continue to work on that progress".
DUP Leader Says Party Won't Agree To Irish Language Act
But she insisted "the basis of an agreement" between the parties and hoped an executive could be "up and running very soon". Sinn Fein's insistence on a stand alone Irish Language Act means that we have reached an impasse.
The new Sinn Fein president said she had met with both the Irish and British governments and encouraged them to "show leadership".
It was widely reported yesterday that a finalised deal was imminent, with both Varadkar and May changing plans in order to be present at talks in Belfast.
But Mrs Foster said while the leaders were welcome, their presence proved a "bit of a distraction" as it interrupted negotiations.
"The best way to do this is for the Irish government to join with us to secure special status for the north within the EU", Anderson said.
"We don't believe there is anything now insurmountable left to resolve".
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