Moyes is due to be out of contract at the end of the season and at one stage early in the campaign it appeared unlikely that he would be offered a new deal.
However, the Scot is now widely expected to sign an extension having led the club to their best-ever points tally at the midway point of a Premier League season.
Moyes, who delivered the club’s first major silverware in 43 years by winning last season’s Europa Conference League, also has his side into the knockout stages of Uefa competition once more, with their Europa League campaign due to resume next month.
The 60-year-old suggested before Christmas that he would hold talks with the club’s owners early in the New Year, and with the transfer window now closed, confirmed negotiations will resume.
"We'll get back on it now the window is shut,” Moyes said. “We're well down the line and moving on with it. We'll pick that up again in the next few weeks."