The Scottish government is being urged to begin preparatory work for a high-speed rail link.
The House of Commons transport committee has backed proposals for a high-speed line between London, the Midlands and eventually Scotland.
HS2 will feature 250mph trains running from London to Birmingham, with plans to extend it north.
The Scottish government has agreed to discuss the funding of the project to develop the route across the border.
The entire HS2 project is set to cost £32bn.
In addition to the connection between London and Birmingham, there are also plans for a Y-shaped extension to Manchester and Leeds, and possibly further north, to be completed about 2032/33.
In its report the transport committee said there was no reason the Scottish government should delay building a section of the track from Glasgow to the border, to connect with the English network in due course.
The committee said the UK government should also consider building southwards and suggests the Scottish government could begin preparatory work on a high-speed line.
The Scottish government said it would discuss funding with Westminster and Transport Scotland said it was ready to start preparatory work.
It has asked for the remit of the UK government's high speed rail company, HS2 Limited, to be extended to include planning for routes to and within Scotland.
Opponents said the report left HS2 "in tatters" because MPs said they could not be sure it would bring the economic benefits ministers predict.
The committee's support for the rail link, which aims to cut the London to Birmingham journey time to 49 minutes, came with a number of provisos.
The committee demanded that ministers "firmly commit" to extending the high-speed link to both Leeds and Manchester before seeking parliamentary approval for the London to Birmingham route.
The Labour chairwoman of the committee, Louise Ellman, said the scheme was affordable and would provide a "step change" in the quality and frequency of rail services between major cities.
She told BBC Radio Scotland's Good Morning Scotland programme: "The best way to ensure it does go to Scotland is for the Scottish ministers themselves to do some work to ensure that that happens.
"We see this as a line for the nation and we think it should not just stop at any one area, that it's important to have increased capacity and better connectivity right across the UK."
Scottish Transport Minister Keith Brown said it was important that the committee had backed the idea of the line extending to Scotland.
He said: "We have to first of all convince the UK government to make sure that the HS2 project team extends its remit to Scotland, because only at that point do you start to get real discussion about routes, technical specifications and planning specifications.
"It's at that point you get real engagement, but we have to get to that point first of all and that's what we're trying to do."
Mr Brown said he expected the UK transport secretary to confirm details of the next stage in the project in December.