Expanding on the issue of borders with the rest of the UK, Alex Salmond says there would be no border controls on travelling from England or Ireland.
But he said there would be controls on people arriving from outside that common travel area.
Minister for Immigration Mark Harper says he will consider more rigorous checks at borders after a report warned that thousands of illegal immigrants attempting to get into the UK through France have not been fingerprinted for four years.
The report by the Chief Inspector of Borders said records need to be kept in case some people later try to claim asylum in the UK.
The Chief Inspector of Borders and Immigration has told ITV Daybreak that a loophole in immigration checks on people entering Britain is "still an issue" and recommends detention facilities at London's St Pancras station to cope with people arriving in this way.
John Vine's comments follow accusations of a "cover-up" by Home Secretary Theresa May after she used legal powers to keep parts of a critical inspection by Mr Vine into UK border controls secret.
In unredacted parts of the report, Mr Vine reveals that border staff remain concerned over the effect of the so-called Lille loophole, which effectively exempts some passengers who travel to Britain via Lille, in France, on Eurostar trains boarded in Belgium, from UK Border Force immigration checks.
Keith Vaz, chair of the Home Affairs Select Committee, has criticised Theresa May's decision to edit out the sections of the borders report dealing with the 'Lille Loophole'.
He said: "I am concerned that the Home Secretary has decided to redact part of the findings related to the 'Lille Loophole', despite John Vine finding that some were still able to reach Britain using this method.
"The committee has been assured in the past that the loophole would be closed. The withholding of information prevents us from properly holding the Border Force to account."
Thousands of illegal immigrants may still be using a loophole on the Eurostar to sneak into the country, a report from a leading civil servant suggests.
However, the Home Secretary has allegedly prevented the public from seeing the sections of the report by Chief Inspector of Borders and Immigration, John Vine, on the "Lille Loophole".
It reveals Border Force staff, who police ports and airports, are still concerned the illegal loophole is being used to get into Britain.
The 'Lille Loophole' exempts some passengers who travel to the UK on Eurostar trains via Lille from British immigration checks.
Nigel Farage has hit out at a report on UK borders after it emerged that sections of the report had been redacted.
The Ukip leader dubbed the removal of 15 sections of the report “extremely concerning” and accused the Home Office of censorship.
Redacted sections of a report into the running of UK borders have been hidden from the public because it would jeopardise national security, the Home Office has said.
The report proved illegal immigrants were prevented from entering the UK by the “excellent working relationships” between the UK, French and Belgian authorities, the Home Office added.
The Home Secretary has been accused of “hiding her own failings” by preventing sections of a report into UK borders from being made available to the public.
Theresa May prevented 15 sections of a report by Chief Inspector of Borders and Immigration John Vine from being published by claiming it was in the interest of national security to keep them secret.
However, the Tory MP was criticised by Labour members for hiding information which shows how many illegal immigrants have not been fingerprinted before entering the UK from France.
Theresa May has come under fire for an alleged “cover-up” of failings at the Home Office and hushed up criticism of how UK borders are run.
Campaigners and MPs accused the Home Secretary of using legal powers to keep fifteen sections of a report into border controls between the UK and France from the public.
One of the sections kept from secret was a passage on fears from border staff at Calais that resources are stretched.
Keith Vaz, the Commons Home Affairs Select Committee Chairman, has said the backlog of outstanding immigration and asylum cases is "spiralling out of control".
In a statement, he said: "There are now about the same number of cases awaiting resolution by UKBA as there are people living in Iceland. The backlog is spiralling out of control."
MPs in the committee added: "We are concerned that the closure of the controlled archives may result in a significant number of people being granted effective amnesty in the United Kingdom, irrespective of the merits of their case.
"For this reason we are concerned that the final checks made on these cases should be thorough and that they should not be rushed to meet an artificial deadline.
"We are particularly interested to find out whether any such individuals would be offered an amnesty or if they would have to start their asylum or immigration application again."