The Football Association is looking at introducing retrospective bans to English football for players who dive or feign injury.
Officials will go on a fact-finding trip to Scotland, where retrospective bans are already used.
In England, players are currently only given retrospective bans for incidents of violent conduct.
It is understood a rule change would require agreement from all football governing bodies in England.
Burnley boss Sean Dyche believes diving would be eradicated from football “in six months” with retrospective bans.
According to a report in Tuesday’s Times newspaper, senior figures at the FA are keen to press ahead with the move.
Dyche’s comments come after two recent incidents in Premier League matches.
Robert Snodgrass apologised for going down without contact to earn a penalty for Hull against Crystal Palace, while Dele Alli won a debated spot-kick in Tottenham’s 5-0 win over Swansea.
At the start of the current season, Hearts’ Jamie Walker was given a retrospective two-match ban for diving to win a penalty against Celtic in the Scottish Premiership.
The Scottish FA found him in breach of disciplinary rule 201 as the “simulation caused a match official to make an incorrect decision”. The player contested the charge, but the compliance officer’s verdict was upheld.
Under current Football Association rules in England, players who pretend to have been fouled should receive a caution for simulation, which comes under the category of unsporting behaviour, if the incident is spotted by the match officials.
However, this can only occur during matches at the moment.
BBC Radio 5 live sports news correspondent Richard Conway
The question of how to deal with players who dive or cheat has long troubled English football.
The law which allows retrospective punishment in Scotland is being examined closely by FA chiefs.
But any changes in England would require agreement from the game’s various stakeholders. That means the Professional Footballers’ Association, League Managers Association, English Football League and Premier League would all need to reach a consensus.
Concerns over player’s cheating is on Fifa’s mind too.
Marco van Basten, the former Netherlands striker who is the world governing body’s chief technical officer, told the BBC last month it is discussing rule changes to increase “honesty” within football.
That could include a rugby style regulation that would allow only the captain to speak with the referee.