Bloomberg, looking to streamline the 911 system, appointed a task force that includes members of all three groups to work out the details, a source said.
The task force, set up in late November, is under orders get a unified system up and running as soon as possible.
The dispatchers belong to different unions, and one source said he anticipates no layoffs.
But labor leaders did not rush to endorse the idea.
David Rosensweig, president of the fire-alarm dispatchers' union, said, "I'm suffering from anxiety waiting to hear how they will divide up these jobs.
"Until that's resolved, I can't either endorse it or support it until I hear my people's jobs will continue and be protected."
There's a possibility that FDNY and EMS dispatchers could be brought into the NYPD's 911 Metrotech headquarters in Downtown Brooklyn by the end of this year.
The FDNY and EMS have never completely merged dispatching operations, even though EMS has been absorbed by the Fire Department.
The FDNY has five dispatching offices - one in each borough - and EMS has its own center in Metrotech.
The NYPD is also hoping to open a second 911 center in Long Island City, Queens, although a site hasn't yet been determined.
