In January, Speak & Go Idiomas sent a letter to the Spanish leader offering him a free course at a language school in England.
The offer was about giving Rajoy the chance to see first-hand the benefits of learning a language in a country where it is spoken, the Madrid-based language school said at the time.
But there was a catch: to take up the chance, the prime minister would have to reinstate language scholarships that had been scrapped as part of his government's cuts to education spending.
Now Rajoy has replied to the school with a letter politely turning down the opportunity.
In the letter, the Spanish leader, who publicly admits his English is not up to scratch, stressed the importance of learning languages, especially English. He also took the chance to highlight his government's push towards bilingual education in public schools as a way of equipping students for the future.
"We never expected that Rajoy would take up the offer of our course. He's in a position of enormous responsibility and probably doesn't have two free days in a row," Speak & Go Idiomas Managing Director Silvía García told The Local.
"But what we really wanted to do is highlight the value of studying languages in the place where they are spoken."
García described the current situation in Spain as "poorly organized" and a "disaster", with the funding situation varying from region to region.
And while students used to get money to go overseas and learn foreign languages, funding cuts meant they were now attending summer camps within Spain.
From 2012 to 2013, the number of scholarships in Spain fell by nearly 25,000 and public schools lost nearly the same number of teachers, according to official data.
"We appreciate Rajoy's vote of support for language learning (in his letter), but more needs to be done," said García.
"Learning a language in situ and studying it in Spain are completely different things and you can't compare."
García was also critical of former Spanish Prime Minister José Luis Rodríguez Zapatero's recent comments that Spanish heads of state didn't need to speak English.
"All politicians need to learn English, and if they don't, they'll always be on the outside and come across as uncultured," she said.
"But I would also say the English-speaking politicians should be studying a foreign language or two.
"It's polite to make an effort to speak another person's language, but learning languages also opens doors. It enriches your understanding of the world," she added.
Spanish leaders have a poor reputation for foreign languages. Zapatero spoke no English, and his predecessor José María Aznar also had a poor command of the language.
By contrast, Spain's King Juan Carlos can speak French, Portuguese, Italian and English.
The former president of the Madrid region, Esperanza Aguirre, is proficient in English and fluent in French.
On the international stage, the English-speaking leaders have some way to go. UK Prime Minister David Cameron speaks a little French but is far from fluent while US President Barack Obama is learning Spanish.