Council tax is likely to go up by almost 4% next year.
Kirklees Council has indicated it is minded to take up the government’s new social care precept.
The move would mean the council could charge an extra 2% on top of the maximum allowed 1.95% increase.
The additional 2% must be used for adult social care in Kirklees.
Councillors were told the social care precept would raise a further £3m for the council.
Householders in a Band D property would see their annual payment rise by about £60.
Councillors have complained that the additional money raising powers don’t even fund the government’s commitment to force them to pay the living wage.
The final decision will be made at the council’s budget setting meeting on February 17.
The bid to increase taxes comes after the council was hit by huge reductions in income from central government.
Last month Kirklees’ leaders found out their grant was being cut by £83m over the next five years.
The reduction comes on the back of £81m in cuts since 2010.