The call comes from the Movement for Married Clergy (MMaC) which fears a celibacy requirement is deterring men from pursuing ordination.
Secretary of the MMaC, Chris McDonnell, told Premier: "The Pope has made it very, very clear that he wants a listening church.
"We're just asking that the bishops of England and Wales listen to the voice of the people because among the laity there is very little opposition to this."
Earlier this year, Pope Francis suggested he was open to Catholic priests being allowed to marry under certain circumstances.
Concerned there is now a "crisis" in priest numbers, the MMaC is calling for a national commission comprising of bishops, clergy and laity to consider the idea.
Some 25 men began diocesan priesthood training for serving in England and Wales last year, significant fewer than in 1985 when the figure stood at 150.
The diocese of Salford announced at the beginning of the year 100 parishes would merge, due in part to declining priest numbers.
Chris McDonnell said merging parishes is not a proper solution, explaining: "It is not fair on a man of 65 or 70 years old to suddenly find he's got not one but two parishes to look after when, in fact, there are other solutions which could give us a better solution to the crisis we are currently facing."
Cardinal Vincent Nichols, Archbishop of Westminster, told the Irish Catholic in February he saw no reason to change the church's rules concerning celibacy.
Click here to listen to Chris McDonnell from the Movement for Married Clergy speaking with Premier's Alex Williams: