A confidential TUC document suggests a much lower limit than the sum backed by most unions and even questions whether they should tie the Labour Party to any figure.
Union leaders are also asked to consider whether a minimum rate should be "phased in".
The new mood at the top of the union movement will be seen as a critical victory for Mr Blair over "old Labour" and will undermine Conservative allegations that a minimum wage will destroy jobs.
While the union movement publicly endorses a rate set at half male median earnings, calculated at pounds 4.26 an hour, a paper prepared for the TUC favours an interpretation of the formula yielding pounds 3.65.
TUC officials would prefer to see no figure mentioned because they believe a sum below pounds 4 would be difficult to get through Congress and any figure above would embarrass Mr Blair.Reuse content