But he added that such advice would not be given until "much nearer the time".
And he repeated the comments he had made after a meeting with the England and Wales Cricket Board (ECB), the game's governing body in Britain, on May 6 that the Government could not force the Board to go back on its commitment to fulfil the tour.
The ECB has already come under intense pressure from politicians to boycott the tour because of human rights abuses allegedly perpetrated by President Robert Mugabe on his own people.
Similar lobbying occurred prior to the World Cup match between the two countries in Harare last year.
Straw rejected calls from the main opposition Conservative party in the House of Commons to attempt to persuade the game's world governing body, the International Cricket Council (ICC), to cancel the tour.
According to regulations drawn up by the ICC earlier this year, England could face a one-year suspension from international cricket and a fine of two million dollars if they decline to tour Zimbabwe on ethical grounds, which would leave the English game effectively bankrupt.
The only way to avoid such stringent sanctions would be if the ICC could be convinced that there were genuine security concerns for the tourists, or if the British Government explicitly ordered the team not to tour.
However, the Government has not imposed any restrictions on British businesses operating in Zimbabwe, and Zimbabwean teams in cricket and other sports have been welcomed into the United Kingdom.
Sri Lanka are currently playing in Zimbabwe, while Australia are about to undertake a tour there after a thorough report into safety and security found no reason for the trip to be cancelled.
Asked in the Commons on Tuesday if the Government could call off the tour on safety grounds, Straw replied: "If there is a security problem which we judge would affect the personal security of English and Welsh cricketers if they go there, then we will make that clear.
"But we have said to the ECB that we need to make that assessment much nearer the time."
Straw added that the issue was wholly different to when the Labour Party had supported the use of sporting sanctions against South Africa during the apartheid regime in the 1970s and 1980s, saying that then there had been an international consensus.
He also said the Government would "prefer the tour to be postponed" and added that he had "great sympathy" for the ECB's position.
But he said: "The Government has no power to instruct people not to leave this country to play sport abroad. We do not have state-run cricket in this country and nor should we."
Zimbabwe, whose team was severely weakened by the withdrawal of 15 white players including former captain Heath Streak, lost last week's first Test at home to Sri Lanka by the huge margin of an innings and 240 runs.
Now, with the 15 'rebels' all sacked by the Zimbabwe Cricket Union, a similarly under-strength side are set to face the Lankans in the second and final Test in Bulawayo starting on Friday.
England meanwhile are set to face New Zealand at Lord's next week in the first Test of a three-match series.