Jose Manuel Barroso, speaking in Berlin yesterday, insisted the EU was stronger with the UK, but said that its specific concerns about its relations with Brussels should be dealt with. However, Mr Barroso does not want this to threaten the European Union's "overall coherence".
Downing Street said his views were indication that significant figures within the EU were engaging with Prime Minister David Cameron's agenda of renegotiation of the UK's membership if he leads the Government after next year's general election.
Speaking at the Humboldt University, Mr Barroso said: "I passionately believe that Europe is stronger with the UK as its member, and that the UK is stronger as a member of the European Union than on its own.
"But I do acknowledge that for historical, geopolitical and economic reasons, the case of the UK may be seen as a special one.
"Precisely because of this, it would be a mistake to transform an exception for the UK into a rule for everyone. We can, and should, find ways to cater to the UK's specificity, in as much as this does not threaten the Union's overall coherence.
"But we should not confound this specificity - even if in some issues it is shared at some moments by several governments - with an overall situation of the Union."
Mr Cameron's official spokesman said: "Does the Prime Minister think that we are seeing evidence of engagement by senior figures from around the EU, such as President Barroso, on his agenda? He very much thinks that. And of course it fits into the Prime Minister's approach for an EU which is not one-size-fits-all.
"The argument around not having a one-size-fits-all approach is very much at the heart of the PM's argument and he is going to keep making it."