Father Ged Murphy, of St Patrick's and St Malachy's, has gained almost 6,000 signatures on his online petition.
He wrote: "There is a proposal by the Spiritual Care Chaplaincy team at North Manchester General Hospital (Crumpsall) to close the Catholic Chapel of Saint Raphael in order to convert it into a Muslim prayer room.
"Worship spaces are going to be provided for Muslims, Jewish people and Protestant Christians, and even a 'Quiet Room' for people of no faith at all!
"Yet it is proposed that Catholics should have no space of their own."
He added that: "St Raphael's Chapel contains the Blessed Sacrament and Mass is celebrated weekly.
"It is well used and highly valued by patients, staff and visitors at the hospital.
"Please stop this valued resource which is much needed when people are at their lowest ebb."
However North Manchester General Hospital has stressed that this is merely a proposal for St Raphael's chapel at the hospital.
Rev John Hall from The Pennine Acute Hospitals NHS Trust said: "As a Trust we recognise how important the provision of dedicated faith and prayer rooms are at our hospitals for our staff, patients, carers and visitors of all faiths, and as such despite some media reports and comments and concerns posted on social media, we can confirm that the Trust has no plans to close any facilities, including the Catholic Chapel here, and we will not be changing or converting this important and well used chapel into any other prayer room.
"We provide a number of chapels and dedicated faith and prayer rooms across our Trust including at the North Manchester General Hospital.
"As part of our efforts to improve our faith and spiritual care services across our hospitals, we are currently looking at how we can improve the access, availability and standard of our facilities for those of all faiths and for all that wish to use them for prayer and reflection.
"We continue to listen and engage with all parties of all faiths to ensure we are meeting the needs of everyone who wish to use our chaplaincy and spiritual care services and facilities.
"More information about our spiritual care and faith services are available on our website at www.pat.nhs.uk.
"I would welcome any comments and feedback on how we can improve access to our faith facilities across our hospitals."
