Len McCluskey, general secretary of Unite, said the union's executive will meet next week to make a decision.
Addressing students at Cambridge University, he said almost half of Unite members did not vote for Labour but were affiliated, which was an "untenable" position.
Unite gives around £3 million to Labour every year by affiliating a million members.
Labour is holding a special conference on Saturday to approve reforms to the link with unions, called for by party leader Ed Miliband.
He wants union members to opt in to join Labour rather than be automatically affiliated.
He made the suggested changes after a row over Unite's involvement in the selection of a Labour candidate in Falkirk.
A Unite spokesman said: "It is a matter for the executive, which will discuss it next week."
The GMB union has already decided to cut its affiliation to Labour after the reforms were put forward.
Last year Unite was embroiled in a row with the party leader Ed Miliband over allegations it tried the rig the selection of a party candidate for the Falkirk Wesminster seat.
It was later decided that individual or organisation broke rules after evidence of wrongdoing was withdrawn.
Labour had sought a new Falkirk candidate following Eric Joyce's announcement he would step down at the 2015 general election after he was convicted of assault at a House of Commons bar.
It investigated allegations that Unite tried to sign people up as party members in the constituency without their knowledge to ensure the union's favoured candidate, Karie Murphy, was chosen.