The Housing Minister says reducing the market rent policy from up to 90% to up to 80% 'doesn't necessarily target help where help is most needed.'
Currently, social rents are set at up to a maximum of 90% market value.
The government says that gives Andium the sufficient income needed to pay for much-needed refurbishment of existing homes and the delivery of new ones.
Former Housing Minister Senator Sam Mezec recently lost a vote to declare a 'housing affordability crisis' in Jersey, in which he asked the government to cut the market rate to 80% from 2022 - which is estimated would cost just under £2million in the first year and more in subsequent years.
Deputy Russell Labey says there are people on the 90% rule who are OK with that payment.
"It's those that are not (on 90%) that we want to target. How to do that is what we're looking at now."
The rule is being reviewed by the government as part of the 'Housing Action Plan' published by the government in June.
The Progress Party, which will field candidates at next year's election, has also announced that it would like to review this rule.
Deputy Labey, who admits he came into the job 'gung-ho' looking to slash the rents to 80% before talking about it to other Ministers and officers, says he understands the feeling that it's hard to defend or justify the 90% figure.
"I will come back (to the States) with all the implications of it and any possible solutions that we might be able to arrive that and the implications for those tenants.
"We will do that before the end of the year."
Sue Duhamel, the Head of Policy, has met Andium Homes and other social housing trusts to discuss this issue and says changing the rule now would have repercussions.
"The level at which you set rents is obviously very important for your overall financial viability of your organisation and Andium has significant loans and debts at the minute, which it is using to fund the refurbishment programme of properties and the current programme to build more units and that is something that everyone is very keen that should continue.
"The decision the States made back in 2013 to set the rents policy where it was - that decision was taken at the time, the argument was made to States members who accepted it was that was the way to fund that particular route of financing the money for the refurbishments.
"We're right in the middle of that process at the minute, so changing that system now will have implications in terms of meeting those extra costs or something else has to give in the way that Andium work their business."
The Chief Executive of Andium Homes says the government's income support scheme needs to be reviewed alongside talks about possibly reducing the 90% rents policy.
Ian Gallichan says reducing the market rate rule from 90 to 80% would be no more affordable and 60% of Andium income is returned to the States, so talks about the 90% rule can't be had without talks on the returns it makes to the treasury.
"The income support scheme as currently set up is effectively saying to the 40% of our tenants who are not in receipt of the housing component, that the income that they've currently got is sufficient.
"That is the debate we need to have - is it sufficient? How many people are in rental stress?
"There is a lot of comment, especially on social media, that says Andium is bankrolled by the income support scheme. It is not.
"What we have got to decide upon as an island is that for Andium to effectively house 4,600 tenants, so that's 10,000 people in our homes, to maintain them, to deliver more homes, we have to have sufficient income."