The Yorkshire Post revealed that the major engineering works in 2019 and 2020 would see the terminus closed on certain weekends.
Trains would instead terminate at Peterborough and East Coast Main Line passengers would likely be offered rail replacement bus travel into London.
Travellers on services from Leeds, Bradford, Wakefield, York, Harrogate, Northallerton, Doncaster and Skipton would be affected.
Closures for the remodelling work at the station will begin in March and continue in June, August and October on selected weekends. There will also be partial closures between Christmas 2019 and spring 2020. Individual platforms will also be shut off at other times.
Plan now for King's Cross closuresSpecific dates have yet to be agreed with Network Rail.
The work will increase the future capacity of the station, but has awkwardly coincided with the introduction of state-of-the-art Azuma trains on the government-run London North Eastern Railway franchise.
Rob McIntosh, Network Rail’s route managing director, said: “Earlier this year the Prime Minister announced significant investment for the East Coast Main Line and our plans at King’s Cross are integral to the benefits this investment will bring for passengers.
“The track layout and signalling at King’s Cross is approaching the end of its design life and restricts the number of trains that we can run in and out of the station.
“We are in the early stages of delivering a project that will increase the number of long distance trains at King’s Cross and facilitate future improvements to journey times.
“We cannot deliver around £250m investment in a confined space such as King’s Cross without some planned disruption. We will make sure passengers have good notice of any service changes to plan their journeys.
“We are also acutely aware of the difficulties passengers have faced across all of our network this year and therefore looking again at the timing and nature of the planned disruption to ensure that the passenger experience is forefront in our decision making.”