Note that this was actually proposed by the EU themselves first [1]. Trump's art of the deal ;)
That being said, since the top 3 producers of gas are the US, Russia, and Qatar, the EU already buys more gas from the US and an arbitrage would be against Qatar (not a bad thing).
All he want's is "a deal" and the ability to prance afterwards.
The deal don't have to be good for the U.S. Trump will say it's a good deal and his supporters believe him. Buying raw materials, oil and gas like US is third world country works well with the EU.
That being said, since the top 3 producers of gas are the US, Russia, and Qatar, the EU already buys more gas from the US and an arbitrage would be against Qatar (not a bad thing).
[1] https://www.politico.eu/article/trump-european-union-gas-lng...