The source says relatives have been praying non-stop for the safe return of Parker, who was snatched at his Parow office on Monday morning as he pulled into his basement parking.
Parker is the fourth wealthy Muslim businessman to be kidnapped in Cape Town in the past two years.
Kidnappers demanded ransom ranging from R10 million to R338 million in the cases of businessmen Sadeck Zhaun Ahmed, Naushad Deshmukh Khan and Mustapha Goolam.
“There have been no ransom demands as yet. No contact made, no calls, no nothing and they [the family] are in a state. Police also have no information for the family yet,” the source tells the Daily Voice.
Parker, 65, of Plattekloof, was snatched by five men in a silver Toyota Hilux double cab bakkie from his offices in Stairway Close, De Greens in N1 City just after 9am on Monday.
The businessman is a founding member of the Foodprop Group, which owns the Foodworld chain of supermarkets.
He and his brother, Rashied, are also partners in a company called FPG Property Fund, among his many business ventures.
In a statement released by the Parker family on Tuesday, they begged anyone with information about the kidnapping to contact police.
The family said they “did not have much to add”, saying they feared for his health.
“Liyaqat is a devoted family man, a known astute businessman who built up business through sheer hard work over many years.
“A community worker, philanthropist, having served as a member of the Friends of The Children’s Hospital Association for several years.
“We are grateful for the outpouring of support we have received throughout the day from various sections of the community.”
The family appealed for anyone with information about “this truly heinous act” to come forward.
“Our father and our brother is an elderly man. So we appeal to those who may be involved or know persons who may be connected with this crime to just release him unharmed before his health deteriorates.”
The family has requested space and time to process the traumatic event.
Family spokesman, Walid Brown refused to answer questions about Parker’s health, or if a ransom has been demanded.
Police said cases of armed robbery and kidnapping have been opened for investigation.
Anyone with info is asked to contact Detective Chesron de Vries on 082 493 8472.