Paqueta has not featured since limping off with a calf problem early in the FA Cup third-round against Bristol City at the start of January.
The Brazilian had, on that occasion, only just returned from a similar issue suffered against Arsenal late last year and Moyes revealed earlier this week that the injury is proving more complex than first thought.
However, speaking after his side’s 3-0 defeat by Manchester United on Sunday, the Scot offered a more upbeat assessment.
“We're hoping that Paqueta is only a week or two away from returning,” Moyes said.
The Hammers have struggled to balance their attack without Paqueta, who had excelled alongside Jarrod Bowen and Mohammed Kudus in a prolific front three during the first half of the season.
Moyes was keen to sign another left-sided forward during the January transfer window but no such deal materialised, while the departures of Said Benrahma and Pablo Fornals have further limited his options.
“We haven’t got into our rhythm, mainly because of some of our boys being away at the Africa Cup of Nations and because of two or three injuries,” Moyes added.
“If we look at our form up until around the first of January, we’ve been very good. But we’ve got knocked off by those things and we just can’t get the balance to our team right on the left-hand side.“