Vladimir Putin set out his demands for a ceasefire deal when he met Trump's envoy Steve Witkoff in Moscow earlier this week, according to a report.
The Wall Street Journal, external, citing officials briefed on the talks, is reporting the Russian president wants Ukrainian forces to pull out of Donetsk and Luhansk altogether, two regions of eastern Ukraine which Russia already controls the majority of.
But the paper said Europeans were pushing for clarity over what that would mean for the Kherson and Zaporizhia regions, where Russian forces also control some territory.
It reported that European officials briefed by the US this week "came away with conflicting impressions about whether Putin intended to freeze the current front lines or eventually pull out of those regions entirely".
BBC News has not confirmed the Wall Street Journal report.
Ukraine has previously said any territorial concessions agreed to without its officials being at the negotiating table would be unacceptable.