The suspension is set to be announced in Strasbourg, France on Wednesday.
The move would mark another escalation in tensions between the US and Europe, as Donald Trump ratchets up his efforts to acquire Greenland, threatening new tariffs over the issue on the weekend. BBC reported.
The stand-off has rattled financial markets, reviving talk of a trade war and the possibility of retaliation against the US for its trade measures.
Shares on both sides of the Atlantic were lower on Tuesday, with European stock markets seeing a second day of losses. In the US, the Dow Jones slid more than 1.7%, while the S&P 500 dropped more than 2% and the Nasdaq closed about 2.4% lower.
Stock markets in the Asia-Pacific region were mixed on Wednesday, with major indexes in Japan and Australia a little lower, while shares in Hong Kong and mainland China were higher.
The price of gold continued to make gains as it rose above $4,800 (£3,570) an ounce for the first time. The price of silver dipped from a record high above $94 an ounce.
Precious metals are seen as safer assets to hold in times of uncertainty, and the prices of both gold and silver have soared over the past year.
On the currency markets, the US dollar held steady against its major peers, having dropped 0.5% overnight - the biggest daily fall since early December.
Trade tensions between the US and Europe had eased since the two sides struck a deal at Trump's Turnberry golf course in Scotland in July.
That agreement set US levies on most European goods at 15%, down from the 30% Trump had initially threatened as part of his "Liberation Day" wave of tariffs in April. In exchange, Europe had agreed to invest in the US and make changes at on the continent expected to boost US exports.
The deal still needs approval from the European Parliament to become official.
But on Saturday, within hours of Trump's threat of US tariffs over Greenland, Manfred Weber, an influential German member of European Parliament, said "approval is not possible at this stage".
And Bernd Lange, who chairs the European Parliament's committee on international trade, said there was "no alternative" but to suspend the deal because of the threats over Greenland.
"By threatening the territorial integrity and sovereignty of an EU member state and by using tariffs as a coercive instrument, the US undermines the stability and predictability of EU–US trade relations," said Lange, whose committee needs to sign off on the deal before it heads to parliament for a final vote.
"There is no alternative but to suspend work on the two Turnberry legislative proposals until the US decides to re-engage on a path of cooperation rather than confrontation, and before any further steps are taken."
