The England and Wales Cricket Board is close to securing a key recommendation which could lead to the reduction of Kolpak players, BBC Sport understands.
At present, players from countries such as South Africa and the West Indies can ply their trade for county sides as if they were domestic players.
But the body lobbying the European Commission for the ECB is confident of a statement which favours change.
The ECB wants to create a bigger pool of players qualified for England.
The name 'Kolpak' came from the Slovakian handball player Maros Kolpak, who in 2004 won a ruling in the European Court of Justice in 2004 allowing him to play professionally in Germany without being classed as a foreigner.
The term has been tagged onto cricketers from South Africa and the West Indies, who are able to come into the UK and play county cricket without being classed as an overseas player.
606: DEBATE
Officially, there is only one 'overseas' player allowed per side in county cricket - but the reality is different.
"It's been a source of real contention for some time," said BBC Radio 5 Live cricket reporter Alison Mitchell.
"Many people believe that these Kolpak players take up the places in county teams which should be going to English-qualified players and thus reducing the pool of talent when it comes to producing players for England.
"I understand that the organisation lobbying the Commission on behalf of the ECB is confident that there will soon be a statement from the Commission which could lead to a situation which would enable the ECB to stop this happening.
"Essentially, they would be free to set their own criteria for such players coming over."
A statement from the Commission is expected in mid-June but, if it is as the ECB expects, it would take much longer for any ruling to come into effect and there could be appeals.
When Leicestershire and Northamptonshire played each other in May, there were no fewer than 10 Kolpak players in the match - with only five on each side who were eligible to play for England.
Some players who would be affected by a rule change include Lance Klusener, Nicky Boje, Hylton Ackerman, Jermaine Lawson and Deon Kruis.
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