Deadline reports that the 43-year-old actor and director Paul Greengrass have entered into discussions with Universal Pictures to reunite for their third movie together in the Bourne franchise.
It's been reported that the film studio intends to move back its next Bourne spinoff sequel, which is set to star Jeremy Renner.
This means that Damon's comeback as the character of Jason Bourne will be released on July 15, 2016, which is a date already assigned to an as-yet-untitled Bourne movie.
As well as releasing a film starring Damon, it's thought that Universal want to release Renner's film in the future and continue the series.
So far, however, Universal has refused to officially comment on the speculation.
Meanwhile, it was reported in June that Damon had agreed a deal that would see him reprise the role of Jason Bourne.
Speaking earlier this year, the actor explained: "I've always been open to it if Paul Greengrass is the director."
Greengrass directed his third of the Bourne films, The Bourne Ultimatum, in 2007.