Elsewhere, two fellow Spaniards who have already beaten him on his favourite clay surface could lie in wait for favourite and defending champion Rafael Nadal at the French Open.
Friday's draw, conducted by Nadal at Roland Garros, also handed women's champion Serena Williams a tricky route.
Almagro surprisingly beat Nadal in the quarter-finals of the Barcelona Open while Ferrer, who the Mallorcan beat in last year's French Open final, knocked him out at the same stage at the Monte Carlo Masters.
"Last week in Rome was tough physically but sometimes you need these things. I played a bit better during the tournament," Nadal told a news conference.
Defeat by Novak Djokovic in the Italian Open final meant Nadal has lost three matches on the European claycourt swing for the first time in a decade, raising doubts over his form.
Djokovic, chasing the only Grand Slam title missing from his collection, takes on Portuguese Joao Sousa in the first round en route to a possible semi-final showdown against former world number one Roger Federer.
Fourth seed Federer plays Slovakian Lukas Lacko in the first round while his fellow Swiss Stanislas Wawrinka, the third seed, faces a tough first round against plays Spaniard Guillermo Garcia-Lopez in round one.
Wawrinka is seeded to meet Nadal in the semi-finals.
Federer, who won the title in 2009, believes there will be little room for surprises at this year's tournament.
"I think at Roland Garros it is a war of attrition, you have to play more shots and you can't rely too much on a good serve to get yourself out of a tricky situation," the 32-year-old told a news conference.
Women's holder and world number one Serena Williams was drawn against France's Alize Lim in the first round before a likely quarter-final clash with Russian Maria Sharapova, whom she beat in last year's final.
Seventh seed Sharapova has been improving greatly on clay over the years and won the Stuttgart and Madrid titles this year back to back. She faces a qualifier in round one.
Second seed Li Na of China, winner in 2011, also faces French opposition in round one in the shape of Kristina Mladenovic. World number four Simona Halep of Romania is Li's potential semi-final opponent.
The top half of the women's draw looks tougher than the bottom with Wimbledon runner-up Sabine Lisicki, Australian Samantha Stosur and third seed Agnieszka Radwanska lurking.
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- Sports & Recreation
- Rafael Nadal
- Serena Williams
- Nicolas Almagro
- David Ferrer