"Our friendship goes back 15 years but we never thought the pope would remember to think of us," she said.
After the nuns realized that they had missed a phone call from the pope, they didn't know what to do. They consulted with their local bishop and tried to call Francis back, without success, the radio network said.
The nuns decided simply to wait in hope of another call.
Hours later, the phone rang again -- and this time they answered.
Frances talked with the community's five nuns, three of whom hail from his native Argentina, on speakerphone, COPE said.
"The message from Pope Francis was to never lose hope, because sadness leads to spiritual sloth and hopelessness," said Sister Adriana.
She added she had known Pope Francis for years and admires his simplicity and closeness to people.
The pontiff's call came on the 400th anniversary of the community.
The popularity of Francis, the first pope from Latin America, is sky-high, a CNN/ORC International poll released last month showed.
Since being elected pope in March, he has made headlines by embracing a humble way of life, caring for the poor and people with disabilities, and reaching out to the gay community.
CNN's Al Goodman reported from Madrid and Radina Gigova from Atlanta. Laura Smith-Spark contributed to this report.