The move would come a little over a year after withdrawing the USA from the the multilateral trade agreement in one of his first acts as president.
But the White House was quick to point out that Trump's decision, rather than a flip-flop, was consistent with earlier statements.
The reason President Trump won the state of Wisconsin is because of the issue of trade and re-entering the agreement would be a direct slap in the face to people who voted for him expecting that he would save their jobs and deliver on economic promises such as ending outsourcing.
"It'll be very good when we get it all finished", Trump said.
According to two Republican senators, the President said during a White House meeting with state law makers and governors that he had "deputised" U.S. trade representative Robert Lighthizer and economic adviser Larry Kudlow to look into the USA rejoining the TPP, in order to open USA farmers to more overseas markets.
And so, Trump on Thursday asked his staff to look at reentering talks on that same TPP, backsliding to the negotiating table after the 11 countries we abandoned recrafted the deal on their own terms. And, experts say it could be good news for Indiana.
But Trump is struggling to get support from other countries for his recent threat to impose import tariffs on China and the US farm lobby is arguing that retaliation by China would hit American agricultural exports. Japan, a close US ally, signed up for the 11-country trade pact. He also has so far exempted the largest USA trading partners from his harshest new tariffs on steel and aluminum.
It was not immediately clear how committed Trump was to embarking on a new path of potentially thorny negotiations.
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Trump pulled the United States out of the agreement shortly after being inaugurated, having put himself at odds with most of the Republican party by criticizing the deal during the campaign.
Japan, the biggest economy in the current version of the TPP, welcomed Trump's comments, with Foreign Minister Taro Kono saying the nation would be "really be very happy if the USA returned". He expressed confidence the United States is headed toward resolving trade conflicts without economic disruption.
Administration officials have said China and the United States can negotiate their differences and avoid a trade war. Beijing has promised to retaliate against the USA with its own tariffs - and is homing in on the U.S. agricultural industry. Senator Ben Sasse told reporters of Trump's remarks on the TPP after the session.
Trump has been critical of TPP, not holding back.
North Dakota Gov. Doug Burgum said Trump made some "pretty positive statements" about allowing the year-round use of E-15 ethanol, which could help corn growers.
But for the rest of the country "it would signal that Trump does not give a crap about working people and can not be trusted on anything".
"I would do TPP if we were able to make a substantially better deal".