Baldwin was speaking in Nigeria where he held meetings with officials from Africa's largest oil producer last week.
He was told that Nigeria was improving security in the Niger Delta and planned to re-open the Trans Niger pipeline after August, which would yield more gas exports to Europe.
The EU imports 14% of its total LNG supplies from Nigeria and there is potential to more than double this, Baldwin told Reuters by phone.
Oil and gas output in Nigeria is being throttled by theft and vandalism of pipelines, leaving gas producer Nigeria LNG Ltd's terminal at Bonny Island operating at 60% capacity.
"If we can get up to beyond 80%, at that point, there might be additional LNG that could be available for spot cargoes to come to Europe," Baldwin said.
"They (Nigerian officials) said to us, 'Come and talk to us again at the end of August because we think we can deliver real progress on this'."
Nigeria LNG is owned by state-oil company NNPC Ltd, Shell, TotalEnergies and Eni.
The European Commission said on Wednesday that EU member states should cut their gas use by 15% from August to March. The target would initially be voluntary, but would become mandatory if the commission declared an emergency.
Last year, Nigeria exported 23 billion cubic metres (bcm) of gas to the EU, but the figure has been declining over the years. In 2018 the bloc bought 36 bcm of LNG from Nigeria, Baldwin said.
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