The trouble is, it's hot in Madrid - 40C these summer days - and for Mr Gonzalez the political temperature is even hotter and rising. Hammered in the European elections, a floodtide of corruption seeping towards him and his domestic popularity at an all-time low, might he change his mind and brave the chill of Brussels?
That is precisely what the German Foreign Minister, Klaus Kinkel, will be trying to find out when he visits Madrid tomorrow on his European tour aimed at breaking the Corfu impasse.
Mr Gonzalez has repeatedly implied he was not in the running for the Delors job and the word here all along has been that Mr Gonzalez never wanted the job. With a normal politician, journalists might be able to cite 'those closest to the Prime Minister', but the trouble with Mr Gonzalez is that no one - not even his wife, the Socialist MP, Carmen Romero, according to media reports - gets close enough to know what is really going on in his mind.
During election campaigning, Mr Gonzalez remains a great communicator. But as for communicating with even his closest aides, that is another matter. Those who claim to know how his mind works say he would have loved the European Commission job - even sacrificing his native Andalucian cuisine for frites-with-everything - until things began turning sour at home. Presiding over the European Commission could have been the culmination of his federalist European dream. Then came a string of serious corruption cases, the resignations of several ministers and closest friends, allegations that he himself may have been aware of some of the corruption cases. In short, the gradual destruction of his previously untainted image. Recent polls show that the Communist, Julio Anguita, is more popular as a political figure than Mr Gonzalez. Mr Anguita's United Left (IU) coalition and the right-wing Popular Party (PP) both won huge gains from the Socialists in last month's European elections.
A weekend poll suggested that most Spaniards believe the Socialist era is over. The conservatives are expected to win the next general elections, scheduled for 1997 but likely to be forced earlier, possibly within the next nine months.
Would the European job tempt Mr Gonzalez to 'do a face-saving Houdini act', in the words of a European diplomat here? The government spokesman, Alfredo Perez Rubalcaba, renewed speculation last week when he said European heads of government were 'putting pressure' on Mr Gonzalez to run for the Commission presidency. The spokesman said Mr Gonzalez had not been swayed but his very reference to such 'pressure' was taken by many journalists as a 'flyer', intended, perhaps, to get the Spanish public used to the idea.
The Foreign Minister, Javier Solana, made similar remarks at the weekend. Mr Gonzalez, he said, would make a 'magnificent' Commission president, but believed he could do more for European union by tidying up his own backyard. Perhaps the most significant comment was that of the Catalan leader, Jordi Pujol. Mr Gonzalez's departure would create 'serious problems', he said, noting pointedly that the Catalan nationalists' vital support for the minority Socialists was based on Mr Gonzalez's leading the Socialists. Without Mr Pujol's support, the Socialists would not have an absolute majority and early elections would be virtually inevitable.
'We are not hostages to Pujol,' insisted the Transport Minister, Jose Borrell. 'Hostage' is a dirty word. But no one can think of a better one.