They will take a formal vote in November.
Artificial surfaces were banned from English professional football in 1995 over issues with ball roll and bounce and fears over long-term injuries.
The proposal was previously aired at a summer meeting in Portugal where a show of hands indicated support.
At the latest meeting, in Walsall, chairmen viewed a presentation at which costs of installing a Fifa two-star-rated 3G surface were examined, along with a variety of other factors including injury rates and competition balance.
Again, they were asked to vote and 29 out of 46 members said they would back the re-introduction.
Rules are now expected to be drawn up and a formal vote on whether to allow them from the start of next season will be taken at the next meeting in November.
Artificial surfaces were allowed in the FA Cup earlier this year.
However, Preston – who installed a plastic pitch at Deepdale in 1986 before ripping it up eight years later – will not be voting in favour.
A PNE spokesman said: “There was a meeting where it was indicated that the majority of clubs would be voting in favour of a return of artificial pitches.
“Preston North End are totally anti the proposals and will vote against it. We were asked to give our views like all the other clubs and as a club we believe it’s not the way forward.
“From a spectator point of view, it’s a completely different game and it also affects the players’ bodies in different ways.”
The vote is also expected to allow the plastic pitches to be used in the Capital One Cup and Johnstone's Paint Trophy.
Plastic pitches were banned from English professional football after four clubs - QPR, Luton Town, Oldham Athletic and Preston North End - tried them during the 1980s.
In July, Conference clubs voted to allow 3G pitches into all three divisions from the 2015/16 season.
English Premiership rugby union sides Saracens and Newcastle and Pro-12 side Cardiff Blues have all installed artificial surfaces, while Super League's Widnes Vikings use one at the Select Security Stadium.
AFC Wimbledon chief executive Erik Samuelson, who was at the meeting, suggested the fan-owned club may look into installing a 3G surface at their Kingsmeadow Stadium.
"I will be taking the findings from the presentation back to the board and we will have a meeting next week with the manager where we will go through the pros and cons," he told BBC Sport.
"For any community club it's a massive plus because it can involve the community. I went to the Allianz Arena and saw fathers and their kids come onto the pitch with a rugby ball - that's a community club. From the community view I am in favour but there are other footballing factors to consider before we decide."
Rochdale chairman Chris Dunphy said it was unlikely such a surface would be installed at the League One club's Spotland home.
"I know [manager] Keith Hill is not keen," he explained. "And they would not be permitted in the Championship so if you got promoted you would have to pull it up. It's worthy of consideration but not something I am widely enthusiastic about."