According to the source, who asked to remain anonymous, Morsi phoned his family last week from a private number.
"I will stand my ground until my last breath," Morsi reportedly told the family in a not-so-short phone call.
Morsi seemed "in high spirits," saying he was following ongoing developments in Egypt, the source said.
It was not the first time Morsi spoke to his family since his July 3 ouster by the powerful military, the source said.
According to the source, the last phone call had come three days after a shorter phone call between the ousted president and his family.
During the phone conversations, Morsi did not provide details about his whereabouts, nor indicate whether the conversations were allowed by the authorities.
Morsi, Egypt's first democratically elected president, has not been seen in public since his ouster.
His family, meanwhile, has not been allowed access to him.
Morsi reportedly told his family that the prosecutors interrogating him were themselves blindfolded so they would not recognize where he was being held.
Morsi faces charges of "conspiring" with the Gaza-based Hamas group to carry out "hostile acts" in Egypt, attacking police facilities and soldiers, and breaking out of prison in 2011.
The deposed leader is also accused of sabotaging public property, along with "killing and abducting" prisoners and soldiers.
"I told them [interrogators] that I'm the country's legitimate leader," Morsi told his family, according to the source.
Mustafa Azab, a spokesman for Morsi's legal defense team, said he was aware of the shorter conversation between the deposed leader and his family, but not of the later, longer conversation.
Azab did not rule out the possibility that both conversations had been sanctioned by the authorities.
Morsi's son, Osama, had earlier said the family was planning to file a complaint with the International Criminal Court in The Hague over Morsi's "arbitrary detention at an undisclosed location."
The family, he added, would not pursue legal action in Egypt since they "don't recognize the [July 3 military] coup or the institutions affiliated with it."