The 49-year-old was given two life sentences in January 1988 after he admitted raping and killing Lynda Mann and Dawn Ashworth, both 15, in Narborough in 1983 and 1986.
Last month he won a two year reduction in the minimum time he must serve before he can apply for parole.
The cut was granted by senior judges who accepted that he was a model prisoner who did valuable charity work.
His legal representatives said yesterday they are now seeking legal advice before deciding whether to seek leave to take the next phase of the appeal to the House of Lords. It is thought they want to appeal for a further cut of between three and five years – meaning the killer could apply for release as early as 2011.
The Home Office ruled in 1994 that he should serve 30 years before he could apply for parole.
A senior judge endorsed that view last year when the case was reviewed again.
Cutting Pitchfork's minimum sentence from 30 to 28 years last month, the Lord Chief Justice of England and Wales, Lord Justice Judge, stressed the killer could only be released when he is no longer deemed to be a threat to the public.
His victims' families have repeatedly said they believe Pitchfork will remain dangerous until the end of his life.