"We would prefer them not to go," said Blair during his weekly question period in the House of Commons on Wednesday.
But he added: "There is a difference between doing that and ordering them not to go which I think would step over the proper line."
He recalled that his foreign secretary Jack Straw would be meeting the England and Wales Cricket Board (ECB) on Thursday to discuss the dilemma.
He added: "I think many people believe, I think rightly, that the problem actually resides with the ICC," the International Cricket Council, the sport's world governing body.
The ECB believes that current British Government advice vis a vis Zimbabwe - where President Robert Mugabe's regime stands accused of human rights abuses - justifies cancelling the forthcoming winter tour.
But it faces a two million pound fine and a one-year suspension if they cancel the tour without the British Government specifically telling them not to travel.