A report to go before councillors at the full council meeting this week lists a number of options for Bearsden Primary and Milngavie Primary.
Both schools require significant investment to address ongoing fabric issues.
Council officers are recommending the option of a full refurbishment of both schools, with pupils decanted to temporary accommodation during the estimated 10-month period of work.
Proposals for each school include a new roof and windows, a full rewire and a replacement heating and plumbing system.
In addition, Bearsden Primary School would have a new modern, fit-for- purpose games and dining hall constructed, with Milngavie Primary having the size of its dining hall increased.
It is understood the proposals by council officers have cross-party support and are almost certain to be signed off by the council’s ruling LibDem/Tory administration.
Joint Council Leader Vaughan Moody (Lib Dem, Bearsden South) said: ‘’I am sure this exciting news will be warmly welcomed by parents, pupils and staff at Bearsden and Milngavie, and of course we will fully consult with them on the proposed programmes of work.
“Our schools in East Dunbartonshire are amongst the best in the country and these latest projects show the administration’s commitment to providing the very best environment in which our young people can learn and thrive.’’
Milngavie Lib Dem councillor Jim Goodall, who is also the Education Convener, added: “I am very pleased at this investment for these two landmark schools.
“It will give both buildings a long and positive future, creating conditions which will be great for teachers and other staff to work in and great for pupils to learn in, too.
“This is work which needs to be done and I am sure that everyone involved with the schools will welcome this news’’.
The council is also expected to give the green light for a new £11.8m replacement building for Balmuildy Primary School in Bishopbriggs.