The UK government wants cricket to take a hard line against Zimbabwe
Support for Zimbabwe appears to be growing in the sub-continent ahead of Wednesday's International Cricket Council meeting in Dubai.
The England and Wales Cricket Board has already stated it will not host a tour by Zimbabwe next year.
And Cricket South Africa has also cut its ties with Zimbabwe because of the political situation in the country.
But India, Pakistan and now Sri Lanka have indicated they will not support a move to expel Zimbabwe from the ICC.
Speaking to the BBC's Sinhala Service, Sri Lanka sports minister Gamini Lokuge said: "I think we should not get sports involved in political issues.
"There has been a military regime in Pakistan for a long time. But Pakistan was never banned from playing international cricket."
He stressed Sri Lanka's policy did not mean the country condoned the political situation there.
But with Sri Lanka adding its support to Zimbabwe Cricket, it is expected the resolution will be defeated at the ICC meeting.
BBC cricket correspondent Jonathan Agnew is in Dubai for the two-day meeting.
He said: "It's such a divisive issue this, there is certainly the thought it could mar the whole of the meeting.
"They could postpone the vote today and get the other items out of the way first.
"The belief is India, Pakistan and Sri Lanka will all side with Zimbabwe. That would avoid their suspension but world cricket could grind to a halt and that does leave a real issue for England and the World Twenty20 next summer.
"They are looking for a compromise position and that could mean Zimbabwe suspending themselves on the grounds of not being good enough at the moment."
Earlier, Niranjan Shah, secretary of the Board of Control for Cricket in India, said: "There is no reason to remove Zimbabwe.
"We understand England's position because their government wants Zimbabwe out but we will back Zimbabwe to stay in the ICC."
The Pakistan Cricket Board, meanwhile, has made it clear it will send its A team on a tour to Zimbabwe in August as scheduled, irrespective of any action taken by the ICC, who have a board meeting on Wednesday and Thursday.
And the Press Trust of India has quoted a PCB spokesman as saying: "We don't think Zimbabwe cricket should face penalties because of political issues in that country. We will not support any sanctions."
Seven of the 10 full ICC members would have to vote in favour of expulsion for such a proposal to go through - and Zimbabwe itself is one of the 10.
If India, Pakistan and Sri Lanka line up alongside them, the proposal would be defeated.
England's hopes of hosting next year's ICC World Twenty20 tournament could thus be put in jeopardy.
We think, in the current circumstances in Zimbabwe, it isn't right for any tour to take place
Although the ICC would not take punitive action against the ECB for preventing Zimbabwe touring in the light of a formal government instruction, refusal to allow a full member to take part in the World Twenty20 could result in the tournament being moved elsewhere.
Such a move would be a huge financial blow to the ECB, with huge crowds expected at the three grounds chosen to host matches. The tournament schedule has already been published and tickets went on sale at 1000 BST on Monday.
The UK government will reassess the situation if the ICC insists that Zimbabwe play in the World Twenty20 but is holding a firm line in its calls for a boycott because of the close links between Zimbabwe Cricket and the regime of president Robert Mugabe.
Culture secretary Andy Burnham told BBC 5 Live's Sportsweek: "The first step is we'll meet the ECB, listen to their report back of the meeting and consider the arguments.
"If we haven't held sway we would listen to the arguments of the other ICC members but our position is completely clear.
"We think, in the current circumstances in Zimbabwe, it isn't right for any tour to take place."
However, he added: "I would not want to be in a position of overruling a governing body in sport. I vigorously defend the independence of our sporting bodies and will always to that."