The idea, which is already being used in Scotland, is on the agenda at the FA's annual general meeting at Wembley on Thursday.
It is understood that the English Football League, League Managers Association, Premier League and Professional Footballers' Association support the plan.
If approved by three-quarters of the 1,100 FA shareholders, three-man panels will review footage from the weekend each Monday and any player unanimously found to have cheated can expect a ban.
Introduced in 2011, the Scottish Football Association's (SFA) rule 201 gives a disciplinary panel the power to impose two-game bans for acts of simulation missed by the officials or rescind yellow cards for players who were incorrectly adjudged to have dived.
Hearts winger Jamie Walker has experienced both verdicts this season, having served a two-game ban for a dive to gain a penalty against Celtic in August and then been retrospectively cleared of simulation during a game against Rangers in December.
Simulation has been an issue in the game for years and there have been a number of notable cases this season, including Robert Snodgrass's dive to earn a penalty for Hull against Crystal Palace and more recent incidents involving Harry Kane and Marcus Rashford.
In January, the FA told Press Association Sport it wanted to talk to the SFA about rule 201 and its impact, but said this was part of a wider discussion with other associations.
In the past, FIFA has been reluctant to take decision-making away from the officials on the day but there are influential voices at world football's governing body more receptive to the idea of technology that helps officials and retrospective penalties to stamp out cheating.
With England and Scotland having permanent seats on FIFA's law-making body the International Football Association Board, bans for divers could soon become a worldwide policy.