Sources say the couple first contacted the company in November last year, around the same time they announced they were leaving the royal family.
According to The Sun, a PR expert has said the couple could earn nearly $2.1 billion from corporate deals and brand ambassador roles, as Harry could be a guest speaker at the bank's Talks at GS series.
It's alleged Goldman doesn't pay guest speakers, but the series could make it possible for Harry and Meghan to form a lucrative relationship with the firm.
Last week Harry appeared at an event in Miami, sponsored by JP Morgan, where he spoke of his mental health struggles after his mother Princess Diana's death.
Critics say working with the firm isn't the best look for the couple. Photo / AP
Experts say JP Morgan paid the couple up to $1.5 million for coming to the Alternative Investment event in Miami.
But the Sussexes faced backlash for attending a summit hosted by a bank that finances fossil fuel companies.
In the past, Harry and Meghan have spoken out against "fossil fuel emissions ... jeopardising" the planet.
They've spoken of a "ticking clock" when it comes to saving the planet.
In 2016 Goldman Sachs paid a $US5 billion settlement for the part the firm played in the 2008 financial crisis.
Goldman and JP Morgan were accused of putting thousands of homeowners in debt with toxic mortgages, while making 10s of billions a year.
Meanwhile, JP Morgan's been accused of putting $117 billion into companies responsible for fracking and Arctic oil and gas exploration.
The American charity Rainforest Action Network came out with the accusation just months before last week's Miami summit, in its Banking on Climate Change 2019 report.
PR expert Mark Borkowski said working with JP Morgan was "not the best look" for the couple. reports The Sun.
"How they accept money, and from whom, is going to be a challenge going forward," he said.
Royal commentator Richard Fitzwilliams also said they needed to be careful.
