"We really don't know any more than we did at Davos [in January] when President Trump said something similar," Parker said.
Since the US withdrawal, the remaining 11 countries have agreed to a new deal called the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP).
It was signed off in March but has not yet come into force.
About 20 provisions of the TPP which the United States negotiated when it was a member of TPP have been suspended, such as keeping copyright at 50 years and not 70, and requiring greater transparency around Pharmac's decision-making.
And some new provisions have been negotiated among the remaining 11, such as narrowing the ability of foreign investors to sue Governments.
Parker said one of the key questions if the US rejoined would be how it would affect these provisions.
"That would be a matter for negotiation."
The provision which allowed New Zealand to ban new house sales to non-resident people living overseas would not be affected, he said.
National Party trade spokesman Todd McClay, who signed the TPP as trade minister, said the US' apparent change of direction was welcome and the Government should engage with US officials as quickly as possible.
However, he said the TPP was a very carefully balanced agreement and Trump's desire for an improved deal could complicate things.
"President Trump wants a good deal from America, which probably means he wants to go much further than the original TPP, and that would create problems for all of the countries including New Zealand.
"For instance, we know that there was great interest from the US around better access for their drug companies in NZ. We were very firm that the Pharmac model was not up for re-negotiation and there would be no extra costs for Kiwis when it came to medicines."
He said none of the US provisions were so significant that they should prevent New Zealand from seeking access to the world's largest consumer market.