Bambino Gesu hospital in Rome says Great Ormond Street Hospital (GOSH) rejected the request to transferred the ten month-old on legal grounds.
President on the hospital, Mariella Enoc said: "I was contacted by the mother, who is a very determined and decisive person and doesn't want to be stopped by anything."
Charlie Gard's parents, Chris Gard and Connie Yates, have been involved in a lengthy but ultimately unsuccessful legal battle involving GOSH, to try and take him to the United States for experimental treatment.
Catholic News Agency journalist in Rome, Andrea Gagliarducci tells Premier such an intervention by Pope Francis is unusual.
He said: "It's very significant because usually pope's do not comment on individual situations although their statements on life, right to life and bioethics issues have been very strong in the past.
"I don't think it's damaging for his reputation because the pope just made an intervention that was based on the social teaching of the church."
Previously, the Pope and US President Donald Trump both expressed their support for Charlie Gard, who suffers from a rare genetic condition and brain damage.
His parents from west London had asked judges at the High Court, the Court of Appeal and the Supreme Court to support their plea; however they ruled in favour of GOSH doctors who recommend that the infant's life-support machine is switched off.
If we can help little #CharlieGard, as per our friends in the U.K. and the Pope, we would be delighted to do so.
— Donald J. Trump (@realDonaldTrump) July 3, 2017
The High Court heard from a specialist who would oversee any treatment Charlie had in the US. They said therapy offered a "small chance" of a meaningful improvement in Charlie's brain functions.
Chris Gard and Connie Yates are currently the last days of Charlie's life with him, after being granted more time before life-support is withdrawn.
Click here to listen to Premier's Alex Williams speaking with Andrea Gagliarducci: