The UK has pledged its support for the territory.
This is arguably the most contentious issue between the United Kingdom and Spain, and a poisonous topic for the upcoming negotiations with the Union as a whole.
Lord Boswell, chairman of the House of Lords EU Committee, said it was "unfortunate that the Prime Minister's letter to Donald Tusk, triggering Article 50, made no mention of Gibraltar - the Government mustn't give the impression that Gibraltar is an afterthought".
Spanish Prime Minister Mariano Rajoy insisted over the last few weeks that when the United Kingdom leaves the European Union, all relations between the European Union and the United Kingdom that affect Gibraltar "must take into account Spain's opinion and have its favourable vote". "[The text] recognises that there are two parties to this dispute".
But he pointed out that, once the United Kingdom leaves the Union, "there is a difference" compared with the previous situation.
The guidelines are due to be formally approved by leaders of the remaining 27 European Union countries at an extraordinary summit in Brussels on April 29. The leaders are expected to endorse them in an extraordinary summit on 29 April.
Picardo, according to the Guardian, said: "This unnecessary, unjustified and unacceptable discriminatory proposed singling out of Gibraltar and its people was the predictable machination of Spain that the people of Gibraltar foresaw and one of the reasons why we voted so massively to remain in the EU". The official was speaking on condition of anonymity to discuss sensitive diplomatic issues.
Express.co.uk has contacted the Spanish Embassy for comment.
"There been a dramatic tone in the way the Spanish are approaching the border issue", he said. It has long sought sovereignty or co-sovereignty of "the rock".
"They have a history of using Gibraltar to deflect from their own internal problems, of which they have had many over the last couple of years, and they continue to have lots of internal problems".
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"There is absolutely no chance that Gibraltar is going to be bartering its British sovereignty, in exchange for continued access to the European Single Market or any one of the other advantages we enjoy as members of the European Union", Fabian Picardo said in NY last October.
The results of several referendums in Gibraltar over the years, the most recent in 2002, have been overwhelmingly in favour of remaining linked to Britain.
Fox said that the Belgian MEP was "frightened of offending Spain".
Close to 99% of the 18,000 people who voted said No.
"Any Brexit agreement without including Gibraltar means there can be no agreement", he said.
In order to remain a part of the EU, Spain offered last autumn to share the sovereignty over the territory.
Picardo has repeatedly rejected the proposal, and did so again on Friday.
Tory MP Andrew Rosindell, of the all-parliamentary group on Gibraltar, said: 'British people must and will stand together, we can not be bullied by Spain.
Mrs May had clearly stated the UK's double-lock commitment never to negotiate on sovereignty against the wishes of the Gibraltarians. "And as part of this, it needs to remind the European Union that it too has a responsibility to reach a deal that protects the interests of thousands of European Union nationals who cross the border from Spain daily to work in Gibraltar".