FFP, designed to stop football clubs spending beyond their means and running up huge losses, has been in place for two years but without any sanctions.
However, a number of second-tier clubs are understood to want the existing rules changed.
Watford chief executive Scott Duxbury recently said that while he agrees with the ethos of FFP, the current plans need adapting, while Brighton have said they would be "very disappointed" if the rules were changed.
Following Tuesday's meeting, a Football League spokesman said: "Considerable progress was achieved on potential improvements to the current regulations following a constructive debate between clubs.
"In particular, there was a focus on maintaining fair competition between clubs, in light of the substantial increase in Premier League parachute payments brought in since the introduction of FFP.
"Clubs also considered the introduction of a 'real time' approach to financial reporting instead of the current retrospective analysis of club accounts."
Discussions are set to continue with three-quarters of the clubs needing to reach an agreement before any rule changes are implemented.
The spokesman added: "The League and Championship clubs will continue developing this work in order to achieve consensus, as any changes to the current regulations will require support from 75 per cent of clubs in order to be approved."