(speaking to BBC News NI, Mr Smith said politicians have “decisions to make but now is the time.”
If agreed, the deal, entitled New Decade, New Approach, could see the assembly reconvene on Friday. Thursday marked three years to the day since Stormont collapsed.
It is the speaker’s responsibility to ensure arrangements are in place for a sitting to facilitate the appointment of an executive.
An assembly spokesperson said: “It is not for the speaker to react to political speculation and he has been clear that whether or not the deadline of (January can be met is a matter entirely for parties.)
“While the Secretary of State for Northern Ireland has requested that the speaker call a sitting of the assembly, the process of doing so remains one for the speaker to undertake in consultation with the parties. “
The statement added:” The speed and timing of any sitting therefore depends entirely on when the speaker hears positively from the parties. “
‘An entirely different construct’
Speaking on the BBC’s Good Morning Ulster program on Friday, Arlene Foster said she was “hopeful” that the DUP and Sinn Féin can restore the executive .
The DUP leader said she had spoken to Michelle O’Neill on Thursday evening.
“Discussions will continue throughout the day and hopefully we can get to a place where we can have the executive up and running again,” she said.
workers across Northern Ireland are going ahead with strike action on Friday, despite efforts to restore Stormont.
Image copyrightPAImage caption The deal would bring about the parties’ commitment to ending ongoing industrial action by healthcare staff
Mr Coveney said the path that led to this point was “based on the extensive discussions and collective work undertaken by the parties since May last year, following the awful murder of Lyra McKee “.
Ms McKee, a journalist, was murdered by the New IRA in April last year.
If the deal is done, the UK government is promising a large cash injection to tackle acute funding problems in Northern Ireland’s hospitals and schools.
The financial annex in the draft deal does not mention any specific figures.
) But last year, the most senior official in the Department of Health said he would need somewhere between £ 728 m and £ 1bn to tackle waiting lists, which are the worst in the UK.
So health service managers will have an expectation that a sum of a least that size will be on the way.
What’s in the draft deal?
Two key sticking points in the Stormont talks were around an Irish language act and the petition of concern.
Image copyrightPA MediaImage caption The call for an Irish language act has been a key sticking point
The draft deal says there is to be “meaningful reform” of the petition, which would be “reduced and returned to its intended purpose” and would “only be used in the most exceptional circumstances and as a last resort, having used every other mechanism”.
The proposed deal would also see legislation created for the appointment of both an Irish language commissioner and an Ulster-Scots commissioner.
It also makes provision for a number of long-standing demands of environmentalists, including the idea that a new program for Government would see a separate climate change act for Northern Ireland – the only part of the UK without such legislation.
Image caption The proposed deal could see the assembly reconvene on Friday
Up until now, Northern Ireland has been bound by and fed into targets set by wider UK legislation.
It proposes an independent environmental protection agency to hold government to account and to ensure compliance with environmental targets.
Image copyright Getty Images 
GIPHY App Key not set. Please check settings