Hours after the European Central Bank launched a huge bond buying scheme aimed at staving off the spectre of deflation haunting continental Europe, Renzi and Merkel sat down to dinner in Florence's Palazzo Vecchio on Thursday night, ahead of a formal summit meeting on Friday morning.
Renzi has made no secret of his hope that the artistic and architectural splendour of his home town will help sway Europe's most powerful leader in a long-simmering battle over the direction of the single currency bloc's economic policy.
The 40-year-old Italian leader believes the budgetary rigour championed by Merkel's Germany has to be balanced by active measures to revitalise the vast eurozone economy, parts of which are mired in recession.
The ECB's dramatic intervention on capital markets was welcomed across the political spectrum in Italy, which stands to receive a substantial boost from the weakening of the euro which most economists expect to follow.
IMF boss Christine Lagarde agreed, saying that ECB president Mario Draghi's move would "lower borrowing costs in the Eurozone, raise inflation expectations and reduce the risk of a drawn-out phase of low inflation", although she added that governments must tighten up their budgets.
In contrast, the central bank's action has provoked 'printing money' misgivings in Germany and Merkel used a speech at Davos earlier on Thursday to warn that the availability of cheaper financing should not deflect debt-stricken governments from addressing their countries' structural economic woes.
"Europe continues to be confronted by great challenges. We have often talked about the debt crisis... we have this somewhat under control but we are not out of the woods yet," Merkel said.
Others in Germany argued that Draghi was putting economic activity in the Eurozone at risk.
"The influence of the programme decided [on Thursday] on the outlook and inflation in the Eurozone is negligible, since interest rates have already reached record lows", DZ bank expert Jan Holthusen told DPA.
"The danger of speculative bubbles arising has been raised".
Germany against the world?
Renzi, a former mayor of Florence, used an interview in the Wall Street Journal this week to warn Germany that it had to seek common ground with its neighbours and partners in the single currency.
"Germany against the rest of the world-this could be a mistake," he told the American financial daily.
The debate over the eurozone's future is being played out against uncertainty over whether Greece will be part of the bloc for much longer.
Most analysts say Greece will most likely stay but Alexis Tsipras, head of the Syriza party tipped to win Sunday's vote, has vowed to ditch EU-imposed austerity measures and seek better terms on the debt the country inherited from two huge international bailouts.
Mother Merkel and little Matteo
Despite their differences, Merkel, 60, and an Italian premier young enough to be her son do appear to have a good personal relationship, with the elder stateswoman frequently praising her younger colleague for his efforts to shake up Italy's labour market, administration, judiciary and electoral system.
Earlier this month, Renzi said in an interview that he hoped dinner in the 14th Century Palazzo Vecchio, a tour of the world famous Uffizi Gallery and a private viewing of Michelangelo's David would help overcome differences between him and the Chancellor, who is a fan of almost everything Italian except their approach to fiscal questions.
"Dostoyevsky used to say that beauty would save the world. Let's see if it can save Europe too," Renzi told La Nazione. Merkel insists good housekeeping is the only way forward for Europe.
"Some people accuse us of being too tight with our money but let me remind you that Germany has a massive demographic challenge," she said in Davos.
"More than six million people will be lost to our market because they are retired. If we don't keep our debts down then we will leave a very heavy burden to the next generation.... This would be irresponsible."