The move follows a decision by the Crown Prosecution Service not to bring charges against the 27-year-old doctor's former boyfriend, Tony Diedrick, despite a judge in a civil case naming him as the murderer.
A lawyer acting for the Francisco family disclosed the plans for fresh legal action as his clients yesterday met with Sir Paul Condon, the Commission of the Metropolitan Police, to discuss their daughter's case.
In a landmark High Court ruling last March, Mr Diedrick, 38, was said by Mr Justice Alliott to have "struck and then strangled" his former girlfriend in her London flat on Boxing Day 1994.
The Francisco family was awarded pounds 50,000 damages against him for assault and battery, although he is appealing against the judgement.
Earlier this month the CPS announced that despite the outcome of the civil case, there was insufficient evidence for a criminal prosecution.
The family's solicitor Taz Raza yesterday said: "I think it's very likely we will go ahead with a private prosecution within the next three or four weeks."
He said the alternative action - a judicial review of the CPS's decision - was also being considered but would probably take too long.
He argued: "The judge at the High Court concluded that Tony Diedrick murdered Joan Francisco. I don't see why if you put the same evidence to a jury of 12 ordinary people they will bring the same conclusion."
Dr Francisco's mother Venus and her sisters Margrette and Celia met Sir Paul at Scotland Yard yesterday.
Following the meeting Scotland Yard issued a statement saying: "The continuing investigation into the murder of Dr Francisco was discussed and it was made clear that police remain determined with their efforts to provide sufficient evidence to prosecute the person responsible for her death."
Mr Raza said: "The purpose of the meeting is to make certain that the file on Joan Francisco is going to be left open, and that the police will continue their investigations and continue to assist us if we do decide to take any private prosecution."
The civil action against Mr Diedrick was the first successful such action to involve someone who had never been charged with a criminal offence.
The case was decided on the civil standard of the balance of probabilities rather than the criminal standard of beyond reasonable doubt.
The decision not to prosecute Diedrick was made jointly by the CPS and the police.