Eurogroup chief Jeroen Dijsselbloem, who is also Dutch finance minister, has been under pressure to step down since he said in an interview published Monday in a German newspaper that southern European countries blew their money on "drinks and women".
Southern Europeans reacted strongly, with Portugal's prime minister and former Italian premier Matteo Renzi calling for Dijsselbloem to step down.
Dijsselbloem's job was already up in the air after his party lost out in elections in The Netherlands last week. His mandate as head of the Eurogroup lasts until January 2018.
Asked if in the wake of the controversy over Dijsselbloem's comments Spain would like the head of the Eurogroup to be Spanish, Rajoy backed Spanish Economy Minister Luis de Guindos for the post in an interview published in several newspapers including top-selling El Pais.
"What can I say. Certainly the Spanish economy minister, if you ask me this, is one of the most important and competent personalities in the Eurogroup," the prime minister said.
De Guindos has served as Economy Ministry in the centre-right government of Rajoy since it took power in December 2011 - the year Spain found itself at the heart of a growing eurozone crisis.
He had to steer through deep spending cuts as Spain tried to rein in its gaping deficit and oversaw a €41 billion ($44 billion) European bailout of the country's ailing banks.
De Guindos was the main challenger to replace Dijsselbloem as the head of the Eurogroup when his first term expired in 2015 but in the end the Dutchman secured his re-election to the powerful post.