England return from their Caribbean tour on April 4 and the IPL's second season gets underway on April 10.
ECB chief executive David Collier has made it clear that since Zimbabwe are due to arrive for a Test and one-day series in April and the squad would need to be rested ahead of that.
''There's a possibility of players playing in the future. But it doesn't look like the period will be longer than 10 days,"Collier told the BBC.
''I think it's common knowledge that the IPL would like more of our players to play ... the question is: which tournaments takes priority at which time of the year? What it does look like is that we will finish our tour to the West Indies and there'll be a 10-day period prior to the players reporting to the first Test match in England,'' Collier said.
However, he said a final decision on whether players can play in the IPL will only be taken in consultation with the team coach Peter Moores.
''Clearly that will be something (England coach) Peter Moores will be looking at, that period of the year to see whether players can play and whether that is a window that will be attractive to the players and to other people in the IPL, or other competitions,'' he added.
But if things stand as they are at the moment, it seems increasingly unlikely that Zimbabwe will be restored to Test status by then.
Even if they are allowed entry into the UK, and that might present an opportunity for a shortened replacement tour starting later in May, or even a brief one-day series against Zimbabwe.