East Lothian Council has confirmed it is in talks with residents of Greenfield Park home for older people and their families over the planned move.
Most, if not all, of the 22 residents at the home are expected to move to the 60-bed facility being constructed at Sanderson's Wynd, Tranent.
A spokeswoman for East Lothian Council said: "I can confirm residents of Greenfield Park have been offered places at the new care facility to be built in Tranent.
"We don't own the building at Greenfield Park and the lease is coming to an end.
"A move to Tranent would mean residents are in a brand new, state-of-the-art facility that is owned by the council.
"We expect the majority of residents will take up this offer. We are continuing to talk to residents and their families about this. We are also looking into alternative arrangements for any residents not wanting to move to Tranent."
She added: "Initial groundwork has started on the Tranent facility and it is expected to be completed by December 2013, with residents from Greenfield Park and Fa'side Lodge (in Tranent) moving in the spring of 2014."
The lease on Greenfield Park, at Monktonhall Terrace, is due to expire around the time residents will transfer to the new home.
Two beds are being made available at council-run Eskgreen care home, on Shorthope Street, for people who wish to remain in Musselburgh. But they will face another move when Eskgreen residents relocate in about 2015 to a new home planned for near the former Tesco site.
Councillor John McNeil (Lab), Musselburgh West member, said: "It is very unfortunate the council made the decision to move people from Greenfield to Tranent.
"I don't know if there is much else the council can do as the new Musselburgh care home doesn't come to fruition until 2014/15.
"As a Labour coalition, we will be looking at this issue with
other members and I will be speaking to the leader of the council to see how we can make it an easier transition for residents and carers."
Permanent staff at the former homes will be matched into posts at the new Tranent facility, while those on temporary contracts can apply for permanent jobs.
The same process will apply for Eskgreen staff moving to the new home in Musselburgh.