Thirteen English league clubs support re-introducing standing at football grounds, according to a fans' group, reports BBC Sport.
On Tuesday, the Football Supporters' Federation is hoping to win the backing of MPs for its plans for a small-scale trial at Premier League clubs.
The Premier League have released a statement opposing the idea.
FSF's Peter Daykin said: "We need to find out if it can work and the only way to do that is to trial it."
But a Premier League statement says they will "not be encouraging the Government to change the law".
It reads: "Since the introduction of all-seater stadia the supporter experience has improved significantly and we have seen more diverse crowds attending Premier League matches, including more women and children.
"The police, safety officers and licensing authorities remain clear and have consistently informed us that crowd management has improved as a result of all-seater stadiums being in place in the top two divisions in this country."
All-seater stadiums have been compulsory in the Premier League since 1994, following Lord Justice Taylor's report after the Hillsborough disaster.
But MP Roger Godsiff has tabled an Early Day Motion calling for government approval of a pilot scheme.
The FSF says the idea has the support of Aston Villa and the Scottish Premier League plus 12 Football League clubs, including Peterborough United, Cardiff City, Crystal Palace, Derby County and Hull City.
The proposal is to introduce a design of "rail seat" currently used in some European countries such as Germany. This incorporates a safety barrier and a flip-down seat on every other row.
The seats can be locked in an upright position, meaning two rows of supporters can stand in between the barriers, which reduces the danger of a crush.
This type of standing area would also be able to be converted to seating for European competitions, where all-seater stadiums are required.