The county council intends to start a procurement process later this month for the £1.1m contract, which will take effect in the spring.
But members of one of the select committees, whose job it is to scrutinise decisions made by cabinet members, said they needed more details.
At a meeting of the health and adult social care committee (HASC) earlier this month, Dr James Walsh (Lib Dem, Littlehampton East) said: “It’s important to know what the details of the new procurement of the contract are and whether it does involve any further reductions in the service.
“It’s difficult to make any comments without those details.”
The current contract is between the county council and the seven district and borough councils, with Central and Southern Sussex Citizens Advice as the lead provider.
Initially the new contract will be for two years, with the possibility of extending it to three.
Amanda Jupp, cabinet member for adults and health, said she would write to each member with the details they required.
But, with her decision due to be made in a fortnight, Anne Jones (Con, Burgess Hill East) asked: “So what time is there to really look?”
Mrs Jones said the advice service was a ‘controversial issue’ in her area, adding: “They are providing less and less times available for the public to use. We’ve just got a couple of sessions a week now, where we used to get something all week.
“It’s difficult for our very vulnerable residents.”