It is understood that Three will meet with Ofcom in the coming weeks.
Any delay to the project, known as the Shared Rural Network (SRN), would also deal a blow to local communities waiting for an upgrade to their critical telecoms infrastructure.
Analysis by consultancy FarrPoint, commissioned by EE, this week revealed that 4G connectivity had delivered economic benefits of up to £6.9m over 15 years for rural communities.
The second phase of the SRN project, which will be funded by the Government, will target “total not spot” areas, where no operators currently provide 4G services.
Ministers have set out a target of covering 95pc of the UK’s landmass by the end of next year and to the entire country by earlier 2027.
A spokesman for Three said: “We are working hard to meet the interim deadline and are on track to deliver the overall January 2027 target for 4G geographic coverage under the SRN programme.”
A BT spokesman said: “We’ve been in discussions with a number of other mobile networks in recent months to share sites to support their own coverage efforts and we’ll continue to collaborate with them on the next phase of the project.”
A spokesman for Ofcom said: “We’re responsible for assessing mobile network operators’ compliance with their coverage obligations, and we expect to receive data about their progress soon.
“Over the summer we will carry out our own analysis, including tests where we’ll drive to certain locations to check that coverage has been delivered. An update on our findings and next steps will then be published in due course.”