The latest talks come as powersharing government in the region has been in flux for a year while the DUP takes protest action against the Northern Ireland Protocol.
The party claims that post-Brexit trading arrangements are a border in the Irish Sea, hampering trade between Northern Ireland and Great Britain, as well as undermining the region’s position in the United Kingdom.
The DUP is refusing to re-enter the Stormont Executive until their concerns over the protocol are addressed.
Separately, negotiations remain ongoing between the UK and EU over the protocol.
On Wednesday, the Supreme Court unanimously ruled that the Northern Ireland Protocol is lawful following a challenge brought by a collective of unionists and Brexiteers.
The latest deadline to re-establish an Executive passed on January 19, placing Mr Heaton-Harris under a legal obligation to call a fresh Assembly election.
In January, the parties were due to meet Foreign Secretary James Cleverly and Mr Heaton-Harris in Belfast.
However, Sinn Fein did not take part after party president Mary-Lou McDonald was not invited, and the SDLP declined to take part in protest at the exclusion of Ms McDonald.
The parties have since met Irish premier Leo Varadkar and Labour leader Sir Keir Starmer.
