Connelly, 40, was jailed in 2008 over the youngster’s death after pleading guilty to causing or allowing the death of a child or vulnerable person.
She was initially released in 2013 but was locked up again two years later after breaking the terms of her indefinite sentence by selling pornographic pictures of herself.
This comes as Dominic Raab, the Justice Secretary, has announced his plans to re-introduce a power of veto over parole decisions involving dangerous criminals.
The power to block the release of high-risk criminals was previously held by ministers but was ended after successful legal challenges in Europe and the UK claimed it was a breach of prisoners’ human rights to let politicians rather than judges determine sentence lengths.
Among those offenders who could be subject to a veto on release by the Justice Secretary are “those who have caused or allowed the death of a child”.