Some clubs are in favour of introducing safe standing areas, following the example of Germany's Bundesliga.
Standing has been banned in England's top two divisions after all-seater stadiums were made mandatory in the wake of the 1989 Hillsborough disaster, in which 96 Liverpool fans died.
But some clubs are in favour of introducing safe standing areas, following the example of Germany's Bundesliga.
West Ham United co-chairman David Gold said the meeting represented "the first steps towards safe standing".
Scottish champions Celtic have installed 3,000 'rail seats' at Celtic Park, which can be folded up and locked, enabling supporters to stand behind waist-high rails.
The ban on standing does not cover Scotland.
"Premier League clubs today held initial discussions on safe standing," a Premier League spokesman said.
"Given that fan safety is of paramount concern, clubs are understandably cautious and there was no overall consensus on the matter.
"This is a complex and emotive topic with a number of issues, varying from club to club, which need to be considered carefully before clubs can decide if they wish to pursue any changes, including legislative, that are required to allow them the option of safe standing areas in their grounds.
"The clubs have tasked the Premier League with scoping out the safety, supporter, technical and legislative? issues surrounding safe standing before any further discussions, based on the facts, can take place."
Ninety-six Liverpool fans were crushed to death on an overcrowded standing terrace prior to an FA Cup semi-final against Nottingham Forest at Sheffield Wednesday's Hillsborough stadium in April 1989.
Hillsborough Support Group secretary Sue Roberts told the BBC it would be a "backwards step" to bring back standing.
Football Association chief executive Martin Glenn said his organisation respected the concerns of the Hillsborough families.
"It's obviously sensitive given Hillsborough," he said. "We've got different history (to Germany). We've had Hillsborough, and they haven't.
"So I think we have got to tread very carefully because our number one duty is to create a safe environment for fans watching football."
The British government's Department of Culture, Media and Sport said there were "no plans" to amend legislation regarding standing at football grounds.