Martinez has been sidelined since suffering the injury during Chelsea's 2-0 Premier League victory over Everton on October 17.
The 34-year-old was forced off following a collision with Everton defender Jarrad Branthwaite at Hill Dickinson Stadium, subsequently undergoing surgery after hospital examinations confirmed a fractured jaw.
His initial recovery period was expected to keep him out for several weeks, but there is now growing optimism that he could return earlier than originally anticipated.
According to The Athletic, Martinez has been consulting a specialist about the possibility of wearing a protective mask, which could help accelerate his comeback.
There remains uncertainty over precisely when he will be available again, but the development offers encouragement to a Chelsea side that has been without its first-choice goalkeeper during an important period of the campaign.
Martinez arrived at Stamford Bridge from Aston Villa in August in a deal reportedly worth £7.5 million.
The World Cup winner had quickly established himself as an important member of Xabi Alonso's squad, making six appearances before suffering the injury against Everton.
He had also kept a clean sheet in the victory at Hill Dickinson Stadium, although the match ended with a disappointing personal setback.
Chelsea subsequently confirmed that the goalkeeper had undergone successful surgery.
"Goalkeeper Emiliano Martinez has undergone successful surgery on a fractured jaw," the club announced in its official injury update.
"Martinez was injured following a collision midway through the second half of our 2-0 victory over Everton at the Hill Dickinson Stadium on Saturday.
"Martinez was taken to hospital for further assessment, which confirmed a fractured jaw that required surgery."
The Argentine's absence has provided an opportunity for Belgian goalkeeper Mike Penders to feature more regularly.
Penders replaced Martinez against Everton before making his first Premier League start in the subsequent London derby against Tottenham.
However, his introduction to regular first-team football proved challenging, with the youngster making an error that contributed to Chelsea's opening goal in their 2-0 defeat at Stamford Bridge.
He subsequently produced a more encouraging display against Liverpool in Wednesday's Carabao Cup fourth-round encounter.
Penders made several important saves as Chelsea held Liverpool to a 1-1 draw over 90 minutes at Anfield, although the visitors eventually lost 6-5 in the penalty shootout.
His performance offered some reassurance to Alonso, who has had to manage the situation without his preferred goalkeeper.
Nevertheless, Martinez's potential return would represent a significant boost for Chelsea as they attempt to improve their results.
The Blues have experienced an inconsistent opening to the Premier League season, collecting 13 points from their first eight matches to occupy fifth position.
Their elimination from the Carabao Cup has added to the pressure, with attention now turning towards Saturday's home fixture against Manchester United.
A return for Martinez would provide Alonso with additional experience and stability at the back, particularly given the Argentine's international pedigree and previous performances in English football.
The manager will nevertheless need to balance the benefits of an early comeback against the risks associated with returning a player from a serious facial injury.
A protective mask could provide a possible solution, but Chelsea have yet to announce a definitive recovery timetable.
For now, the reported progress is encouraging, although Martinez's availability for the coming fixtures remains uncertain.