Asked if he could reassure the Israeli leader that he would not be arrested if he came to Britain, Straw at first hesitated.
"I think so, although let me say these are all matters for the courts and not for me," he told BBC television in an interview on Sunday.
His comments may lend credence to a report in The Times on Saturday that said Sharon had snubbed an invitation from British Prime Minister Tony Blair to visit London, claiming he feared arrest.
The paper said Sharon cited the case of a former senior general, Doron Almog, who avoided detention this month at London's Heathrow airport on war crimes allegations after a human rights group lodged charges that cannot be brought in Israel.
Straw said Sharon had visited Britain on previous occasions and some people had tried to "stir up trouble against him".
"But these have not come to fruition and I doubt very much indeed that they will come to fruition again," he said.
"Moreover, he is a serving prime minister in a very different capacity from somebody who had retired from the Israeli army."
Almog has been accused by Palestinians and Israelis on the left of the political spectrum of breaching international laws during Israel's occupation of the Gaza Strip.
Blair's office declined to comment, and no one was immediately available at Sharon's office to comment.