Despite suggestions that the first lady had returned to Zimbabwe on Tuesday, South Africa's police ministry said she remains in that country and has indicated plans to attend the regional bloc's summit, which officially opens on Saturday.
South Africa, which already hosts a large population of Zimbabwean refugees, is anxious about the fallout from an accelerated collapse of the Zimbabwean regime as well as backlash from domestic voters who support Mugabe, a one-time liberation hero who still casts himself as the persecuted foe of western imperialism.
A police statement said the Zimbabwean government has asked for diplomatic immunity for a suspect involved in the assault.
Her whereabouts were not known on Thursday although police minister Fikile Mbalula said she remained in the country.
South African police issued a "red alert" on Friday at the country's borders to prevent Mugabe from fleeing undetected. Her added that the family is not interested in pursuing that route.
Officials, however, refused to comment on what this programme involved or if it would still be taking place.
The alleged beatdown left Engels with a nasty gash on her forehead that required 14 stitches.
However, her daughter's legal team - which includes Gerrie Nel, the prosecutor who secured a murder conviction against Olympic and Paralympic track star Oscar Pistorius - would counter such a move, she said. Nel said this at an AfriForum media briefing in Centurion. "It's about justice", he said.
It had since come to light that the Engels family was approached by a third party, offering them money not to pursue charges against Mugabe.
Cathleen Powell, a senior public law lecturer at the University of Cape Town, explained that legally, the first lady has no grounds got justification as she was not an accredited diplomat and couldn't claim immunity.
He said no amount had been mentioned - just an offer - 'let us talk and this can go away'. And lawyers working with the model say they will consider making an urgent application to South Africa's courts in the next few days, insisting that diplomatic immunity can't be used to "escape prosecution from grave crimes".
It's not clear what the three were doing that upset the first lady, but Engels says Mugabe began beating her with an extension chord.
'If they can't prosecute #GraceMugabe then they must make sure her sons and her don't return to SA, ' one Twitter user said.
It is not the first time Mrs Mugabe has faced legal action. Zimbabwe's ambassador to Pretoria, Isaac Moyo, did not answer his phone.
The group has sought to block any attempt by government officials to grant Mugabe diplomatic immunity.