The two sides last met at the 2007 World Twenty20 in South Africa
The British government is considering preventing the Zimbabwe cricket team touring England next summer.
But a blanket ban on all sports stars from Zimbabwe competing in the UK is no longer on its agenda.
Prime Minister Gordon Brown is keen to take a tough stance against President Robert Mugabe but only cricket is being targeted, say government sources.
The government will also wait until the outcome of the general election in Zimbabwe before making a decision.
The BBC's Inside Sport programme revealed on Monday that the goverment was considering four options to prevent the Zimbabwe team competing in England:
- Option One: The ICC bans Zimbabwe from international cricket, or the ECB reaches a deal with the Zimbabwe Cricket Union to call off the tour.
- Option Two: Stop bilateral tours, thus scrapping the proposed Test and one-day series, but allow Zimbabwe to compete at the World Twenty20 later on in 2009.
- Option Three: A blanket ban on any team representing Zimbabwe from competing in the UK, thus excluding them from the World Twenty20 as well.
- Option Four: A ban on ANY Zimbabwean from competing at a sports event in the UK.
The latter, by far the most radical, would, for example, prevent Cara Black from defending her women's doubles title at Wimbledon.
But the Prime Minister's spokesman said on Tuesday that No 10 had been "surprised" by the report suggesting that Gordon Brown was considering a ban.
"It is not the case that the Prime Minister is considering a blanket ban on Zimbabwe's sportsmen," said the spokesman.
He added that it was a matter for the English cricket authorities to decide whether a planned tour by the Zimbabwe cricket team went ahead.
"If they decided they want to ban Zimbabwe, we would support them," he said.
We should not let international sport become a propaganda tool for dictators
A spokesman for the Department of Culture, Media and Sport
A spokesman for the Department of Culture, Media and Sport said: "Our position hasn't changed and no decisions have been taken, though the matter of cricket tours with Zimbabwe is under review.
"We are keeping in close contact with the ECB on the matter.
"While there are currently no sporting sanctions on Zimbabwe, we should not let international sport become a propaganda tool for dictators."
Zimbabwe's Information Minister Sikhanyiso Ndlovu told the BBC that any ban of all Zimbabwean sporting competitors from the UK would be "racist" and "madness".
"I don't think the British Government will sink so low as to implement that - and if they do, well, we are appealing to the world community to express their concern and urge the British to stop that madness," he said.
Zimbabwe's cricket side are due to play two five-day matches and three one-day internationals next summer.
The England and Wales Cricket Board would have to pay an estimated £225,000 in compensation under ICC rules if the one-day matches are cancelled.
The ECB has already held talks with Zimbabwe Cricket to try to reach a financial settlement to call off the tour.
There would be no penalty for scrapping the five-day games as Zimbabwe is no longer classed as a Test-playing nation.
An ECB spokesman said the board would not comment until it had discussed the matter with government officials.