Manfred Weber, a senior MEP, poured cold water on hopes of a breakthrough at a crunch European summit next month.
The comments came as Brussels ramped up pressure on the Prime Minister to agree to demands for a huge divorce bill.
A failure to get the green light from national leaders at the December gathering would mean discussions about future trade arrangements could not begin before March - raising the risk of the UK leaving without any deal.
EU negotiator Michel Barnier last week gave Britain just two weeks to put more cash on the table to secure a divorce deal in time for future trade talks to start next month.
The two sides are engaged in a bitter stand-off over the size of the divorce bill - with the UK offering around 20billion euros during a transition phase, but the bloc insisting the figure must be triple that figure.
There are fears that failure to reach an agreement before Christmas could lead to a 'no deal' Brexit and cause severe harm to economies.
Business on both side of the channel has become increasingly anxious about the prospect of political deadlock disrupting trade.
German Chancellor Angela Merkel is coming under pressure to protect her country's car exports - with Britain a key market.
Speaking to journalists in Brussels this morning, Mr Weber said: 'In December, it doesn't look like negotiations are going to move onto the second phase to talk about the future.'
He added: 'Theresa May has asked for talks — she knows that the negotiations are in a decisive phase.'
Guy Verhofstadt, the EU parliament's chief negotiator, also increased the temperature by demanding that EU citizens are given 'the exact same rights as they have today'.
'Our aim is nothing is changing. They can simply continue rights as they have them now,' he added.
'For European Parliament and steering group inside European Parliament, our priority is to have a good arrangement on citizens' rights.
'Not only rights of EU citizens in the UK but UK citizens in the EU. What we absolutely want to avoid is citizens being victims of Brexit,' Verhofstadt explained.
'What we absolutely want to avoid is citizens being victims of Brexit.'