ALBANY – Top state officials are negotiating a package of income tax breaks aimed at middle-class New Yorkers and are closing in on plans to hike the state tax deduction for household dependents and boost the child tax credit.

At the same time, the sides are suddenly discussing an extension of an income tax surcharge on upper-income individuals and couples, state officials said. That surcharge, worth nearly $2 billion annually to Albany, was enacted in late 2011 and is due to expire in 2014 – the same year Gov. Andrew M. Cuomo and lawmakers will be up for re-election.

The emergence of the tax cut package, which could be tied to a hike in the state’s minimum wage, came as lawmakers left town Thursday night with plans to return Sunday or Monday for a final round of closed-door meetings before budget bills are printed.

Sources close to the talks say all sides – a coalition group in the Senate, Assembly Democrats and Cuomo – are trying to make the tax cut package happen in a 2013 budget that has otherwise generated little major controversy.

Officially, government leaders were keeping to the annual news blackout practice that is the traditional sign of progress at the negotiating table. “Discussions are ongoing,’’ was as specific as Assembly Speaker Sheldon Silver, a Manhattan Democrat, would get after emerging from closed-door talks with Cuomo and Senate leaders.

But privately, sources say the tax cut package and a larger-than-expected hike in aid to public schools will emerge as the major points all sides will tout if the deals come together. Officials are looking to start printing budget bills so work can be complete by next Thursday or Friday in what would be the earliest state budget adoption in more than 35 years.

The plan being eyed, first floated by Senate Republicans, would raise the income tax credit parents could take from the current $330 per child. What the level would be is still under discussion, and Senate Republican leader Dean Skelos said that Thursday the various options were being calculated.

Officials say they also are trying to nail down a final deal on raising the current tax exemption on dependents; the level is now $1,000 per dependent, and backers say the child tax credit and dependent exemptions have failed to keep up with inflation for years.

How big the personal income tax cut package will be depends on how fiscal staffs can fit together the wish lists on spending and tax cuts.

Cuomo mentioned the child tax credit issue is on the table. “If we have an option to reduce taxes in this state, I’m certainly open and aggressive about it, but nothing is in and nothing is out,’’ Cuomo told reporters Thursday night.

Lawmakers earlier in the day agreed to $550 million in an overall restoration pot, some of which is new money and some of which is reconfigured funds from what Cuomo proposed in his budget. The majority of the additional funds are being earmarked for state aid to New York’s 700 school districts.

Cuomo appears especially eager to be able to tout the possibility of attaining three straight years of on-time budgets, but Thursday night he sought to lower expectations of meeting the April 1 deadline just in case some unforeseen problems arise in the talks.

The sides have failed to nail down a deal on raising the minimum wage, which is now $7.25 per hour. But, significantly, Senate Republicans have dropped their former staunch opposition and appear willing to trade an increase for items they want, including personal income and business tax cuts.

At issue is how much of a hike there will be, if it will be phased in over a period of time and if future increases will automatically adjust to the inflation rate.

“It’s on the table,’’ Silver said of the minimum wage issue. Off the table, all sides seem to agree, is legislation to specify the terms of how the state might expand gambling by permitting up to seven new casinos in New York. Lawmakers insisted Thursday there is neither the time nor willingness to take up that matter now and say it would jeopardize getting a budget done in time. They say the issue can be dealt with later in the session.

Though he did not propose such a plan when he unveiled his 2013 budget proposal in January, Cuomo on Thursday spoke about trying to do as much of a two-year budget plan as possible this year. He called that a smart way to plan the state’s finances but noted it could be especially bumpy given the unpredictable spending and tax revenue trends.

Doing a partial two-year budget plan also could provide some political cover to extend the 2011 income tax surcharge on wealthy New Yorkers without having to go through the tax hike route all over again. In 2011 Cuomo had flatly said he would not raise the tax, saying it would hurt job-creation efforts; he backed down in a December 2011 deal with lawmakers. Although it is called the “millionaires tax,’’ the surcharge actually starts on individuals making over $200,000 a year.

An assortment of final issues still must be resolved, from how much to restore in cuts to programs serving developmentally disabled people to whether people ticketed for speeding can plea-bargain the violations down to a parking ticket.