His comments come as leaders of the three big Eurozone countries, France, Germany and Italy, met on Monday on what action they should take to counter mounting Euroscepticism, of which the Brexit vote is the most dramatic example.
Italy's Prime Minister Matteo Renzi welcomed the German Chancellor, Angela Merkel, and the French President, François Hollande to Ventotene off the coast of Naples for a second round of trilateral talks before an informal EU summit in September.
The question of similar breakaway movements in other northern European member states is expected to be raised at Monday's get-together
The fallout from the Brexit referendum is expected to feature near the top of the diplomatic agenda for most of the coming week.
Ahead of Monday's meeting, Roth said, "Given Britain's size, significance and its long membership of the EU, there will probably be a special status which only bears limited comparison to that of countries that have never belonged to the EU."
"I want relations between the EU and Britain to be as close as possible," he said, but added: "There cannot be any cherry picking."
Asked if Britain could retain the same level of market access while putting limits on the free movement of people, he replied: "I can't imagine that."
Roth, a member of the centre-left SPD party, suggested that it should be possible to complete the negotiations within two years and that they should be started in time to ensure that Britain leaves before the next elections for the European Parliament in 2019.
"Even if we didn't want or hope for it, Brexit won and, as it won, there can't be any British members in the next European Parliament," Roth said.
With the fallout from the EU referendum vote only now starting to be felt, Scottish Nationalist MEP Alyn Smith has said that Scottish people should decide whether the country continues as a monarchy or a republic.
When asked where he stood on the issue of "monarchy versus republic", he said, "I want to see the people of Scotland in charge of Scotland's future, so once we regain independence I would be up for a referendum on the subject and the people will choose, but let's do it after independence so we can have a proper debate about the subject in its own right."
His comments come after SNP leader, Nicola Sturgeon, said another independence referendum is "highly likely" after the UK voted to leave the EU against majority opinion in Scotland. Some polls have recorded that a majority of citizens are now in favour of leaving the UK.
Several years ago, the SNP published a draft constitution for an independent Scotland, stating: "The SNP is committed to holding a referendum in the term of office of the first independent Parliament of Scotland on whether to retain the monarchy."
After the Brexit vote, Smith received a standing ovation from MEPs after he begged them not to "let Scotland down".
The UK voted by 52 per cent to 48 per cent to leave the union after 43 years of membership and Smith used a speech in Parliament before the summer recess to urge the EU to respect the will of Scotland, after its electors voted by 62 per cent to 38 per cent to remain in the EU.