East Renfrewshire Council is to move forward to the next stage of the proposal following successful talks with faith leaders.
If the go-ahead is given to find a potential campus site in Newton Mearns, formal consultation will start in the spring.
The £13.6million campus would be a replacement for East Renfrewshire's existing Jewish primary, Calderwood Lodge, and provide an additional Catholic primary alongside St Cadoc's.
The council agreed last October to hold an informal consultation with the Catholic and Jewish communities.
Director of education Mhairi Shaw met parents' groups from Calderwood Lodge and St Cadoc's, as well as school chaplains.
Meetings have been held at churches while parent councils had joint talks.
The council said feedback from organisations such as the Glasgow Jewish Representative Council and the Catholic church had been positive. Now both communities say they are in favour of the shared campus proposal.
There is already £10m in the council's capital plan for a new Catholic primary, which the council has had in the pipeline for some time, but to create a shared campus would cost an additional £3.6m.
Councillor Paul O'Kane, vice-convener for education, said: "It is hugely encouraging both communities have responded to this informal consultation so positively.
"There is a pressing need for additional school places for children of Catholic faith, and our Jewish school community has long expressed the desire to relocate to East Renfrewshire, where most Calderwood Lodge pupils live.
"I look forward to hearing more positive and encouraging views from everyone."