Neither side has yet given way on the future of St Aloysius primary and Chapelhall Primary - with the Roman Catholic Church still arguing that a roll of 300 justifies the continuation of St Aloysius as a stand-alone denominational school, and the council sticking by its argument that the two schools should share a single campus.
A spokesman for the Scottish Catholic Church said: "The thing that has changed in the last 10 days is that there is definitely a renewed willingness to solve the problem."
It is understood that the latest round of talks has been led by officials, with religious and political leaders stepping back from the fray. Last week, the diocese announced that it was dropping its petition to the Court of Session seeking a judicial review of the decision that ministerial consent was not required for the joint campus proposals.
The two sides issued a joint statement announcing that agreement had been reached on the design and layout of five proposed shared campus developments - Glenboig primary and Our Lady and St Joseph's primary; Glengowan primary and St Mary's primary; Plains Primary and St David's primary; New Stevenston primary and St Patrick's primary; and Wishaw Academy primary and St Ignatius' primary.
Agreement is understood to be very close over the final design of the St Kevin's primary and Bargeddie primary shared campus development.