The real estate tycoon used a speech during his visit to the World Economic Forum in Davos to make his suggestion, only days after the 11 countries also in the deal agreed to move ahead with the blockbuster accord, minus the US.
The signal, although vague, was well received by the free-market loving audience, which included the who's who of the world's economic and political elite.
Dumping the Trans-Pacific Partnership (TPP) was one of Trump's first decisions after entering the White House, under the belief the accord would punish US workers by allowing companies to hire cheaper labour abroad.
The Trans-Pacific Partnership (TPP) was initially a US-led project that if finalised, would have accounted for 40 percent of global GDP, while deliberately excluding Washington's regional rival China.
Trump's predecessor Barack Obama believed the deal would set a higher standard for trade, including on health and the environment, and eventually entice China to play by the same rules.
In his speech to the packed audience in Davos, Trump said the US would consider negotiating trade deals with its onetime TPP partners "either individually, or perhaps as a group."
But only "if it is in the interests of all", he added.
'Big deal'
Audience members warmed to the comments, hoping that it may mark a small but significant pivot from Trump's "America First" protectionist mantra.
Asked whether Trump's change on the TPP, which he first indicated to CNBC in Davos, would be followed up with real proposals, a senior US official said: "There will be follow-through."
Trump "sent a very important signal about TPP... That's a big deal for the region," Singapore's former diplomat to the UN Kishore Mahbubani told AFP after the speech.
Trump's pullout "was a disaster, because it would have helped anchor the American president in the region," he added.
EU Commission Vice President Jyrki Katainen, the most senior official from Brussels to attend the speech, said it was "always positive if the US wants to be part of the free trade agreements."
Though "I don't really know what he means, renegotiate or have a new agreement", he added.
Trump's visit in Davos was preceded by the appearance earlier in the week of Canadian Prime Minister Justin
Trudeau, who celebrated the announcement of the rejuvenated Asia-Pacific trade agreement.
The 11 members are expected in March to finalise the deal, which was revived after a big push by New Zealand and Japan.
The original deal included removing a slew of non-tariff restrictions and required members to comply with a high level of regulatory standards in areas such as labour law, environmental protection, intellectual property and government procurement.
Without the United States, TPP-11 only represents 13.5 percent of the global economy.
Ten top quotes from Trump day at Davos
Global movers and shakers flocked to hear US President Donald Trump speak on the final day of the week-long World Economic Forum in Davos, Switzerland on Friday. Here are 10 top quotes of the day:
First among equals?
- "America First does not mean America alone. When the United States grows, so does the world."
- Trump woos Davos with an uncharacteristic gesture of openness.
Everyone for himself
- "Just like we expect the leaders of other countries to protect their interests, as president of the United States, I will always protect the interests of our country, our companies, and our workers."
- Trump returns to familiar ground.
Back in time
- "If each country is narrowly pursuing its agenda, it will clash with the agendas of others, and we will take the world back to 1913 once again."
- UN High Commissioner for Human Rights Zeid Ra'ad Al Hussein, in response to 'America First'.
Be nice
- "As a businessman I was always treated really well by the press... it wasn't until I became a politician that I realised how nasty, how mean, how vicious and how fake the press can be."
- After turning on the charm in his speech, Trump goes off-script in a question-and-answer session with forum chairman Klaus Schwab.
Hiss
- "Boo!"
- Some audience members' response to Trump's attack on the media.
Come in peace
- "It was positive in the sense that he didn't declare any trade war, or any other wars... It was more consensual than many of us may have expected."
- European Commission vice president Jyrki Katainen.
'Rational' Trump?
- "It's a middle-of-the-road, unexciting, rational speech. It was not at all what you expect from Donald Trump, who sometimes makes very wild statements."
- Singapore's former UN ambassador Kishore Mahbubani.
Africans for Trump
- "In private we love Trump. There is something in the way he does things, his disruptive nature, his aggressiveness, which is what business is all about. So quietly we want to be like him, while publicly that's an embarrassment."
- Paul Okumu, Kenyan head of the African business and development group Africa Platform, after the US president this month reportedly used insulting language to describe African countries.
Forget him
- "President Trump's boastful sales pitch was a victory lap for the trillions of tax cuts that the wealthy elites and corporations have clamoured for... The president who claims to be fighting for the forgotten men and women is really seeking the approval of the world's elites."
- Oxfam's executive director Winnie Byanyima.
End of days
- "Davos is a good place to announce that their days are numbered."
- Billionaire investor George Soros warns tech giants such as Facebook and Google they must be regulated or die.
