The Cabinet paper said that figure reflected the large number of trees planted in the 1990s which are coming up for harvesting over the coming years.
Jones has previously said the Government's 1b goal would be a collaborative effort between the Government and the private sector.
But National economic development spokesman Paul Goldsmith said it was clear that counting business-as-usual private sector planting towards the total was trickery.
"This Government has made massive promises and now they're starting to walk them back. Not even Shane Jones himself believes they'll [the Government] plant 1b trees."
Jones told the Herald he was confident that between the work the Government was doing, and the increasing buy-in and support from the forestry industry, that planting 1b trees over 10 years remains a very attainable goal.
"Let's see if we can get more than a billion trees in the ground, eh?"
In August last year, Jones announced the Government would pour an extra $240m from the Provincial Growth Fund (PGF) into the 1b trees initiative.
This was on top of the $245m which had already been allocated from the PGF to the scheme.
This funding, announced in August, would be spent in three tranches: $62m in 2018/19, $84m in 2019/20 and $97m in 2020/21.
But Jones said in the Cabinet paper that more money may still be required.
"I will report back on any additional funding requirements beyond the first three years of the programme once there is further information about the take-up and impact of the investments and regulatory changes," he said.
In addition to the trees expected to be planted by the private sector, some 125m would come from tree planting grants and between 102m and 170m would be planted due to regulatory changes, according to the Cabinet paper.
Te Uru Rakau, Forestry New Zealand, boss Julie Collins said the 1b-1.4b estimates were actually conservative, as the department expected a higher number of landowners would turn to planting trees once new incentive schemes were in place.
She also said changes to the Emissions Trading Scheme, which she said was expected to be in place from late 2019, would also drive an increase in tree planting.
As of January this year, nearly 61m trees have been planted – surpassing the 55m goal.
Jones joked that the tree counter had been fitted with energiser batteries.
"It's been tracking steadily and positivity and now it's into growth phase – and I'm not counting hemp or medical marijuana."