Kenny MacAskill said he is "actively considering" the move after a damning review revealed a catalogue of failings by the authorities that allowed Ryan Yates to attack the woman less than a week after his release from prison.
The pensioner, who cannot be named for legal reasons, backed the change and said her "nightmare ordeal" would never have happened if the serial sex offender was being tracked by the authorities.
The review of Yates's case found he was freed from prison despite it being "clear" that he was likely to reoffend and there being no management plan in place to reduce the risk he posed to the public.
Yates was not made the subject of a Sexual Offences Prevention Order (SOPO), which could have required him to stay away from areas like schools and playgrounds, until two days before the attack in Aberdeen.
Had this been in place earlier, the review found that the paedophile may have been returned to prison before the attack as he admitted approaching children near a park, buying a knife set and "hunting for a victim".
He pleaded with social workers to allow him to buy a knife on the day of his release and they failed to report him spending much of his time at a supermarket staring at children.
But, despite the authorities missing a series of warning signs, the report concluded that Yates is "solely" responsible for his crimes and the criminal justice agencies performed to the expected standard.
It recommended that Mr MacAskill introduce satellite tracking of sex offenders, a change the minister confirmed he was considering, but he rejected another proposal to impose lifetime monitoring restrictions after the offender has been sentenced.
The grandmother, who bravely managed to protect her grandchildren, said yesterday: "This would never have happened if a tracking device was in place.
"We would never have had to go through our nightmare ordeal. This new device could save other people from going through what I did."
The review, conducted by the Highlands Multi Agency Public Protection Panel (MAPPA) examined how Grampian Police, Aberdeen City Council and NHS Grampian managed Yates' release and makes 18 recommendations.
The 31-year-old was released from Aberdeen's Craiginches prison in October 2009, where he was serving a seven-year sentence for a sexually-aggravated assault. He had been in custody almost constantly since the age of 14 for sexual offences.
He was jailed for a minimum of 10 years for the knife attack on the 60-year-old pensioner but judge Lord Pentland told him he will probably never be released.
Given his previous pattern of reoffending, the review said he posed a "very high" risk but no "comprehensive risk management plan" was drawn up for his release despite the authorities recognising the danger he posed.
Grampian Police only submitted an application for a SOPO a week before he was freed, meaning it was not presented at court until four days after his released.
Prison treatment programmes aimed at altering the behaviour of sexual offenders "do not address sexual preoccupation, deviant sexual preference for children or preference for sexualised violence," the review team found.