"If the main thing is Donetsk and if there are no concessions, we should not continue this whole thing," the Axios source quotes Trump as saying.
Then Putin allegedly abandoned his demands.
US intelligence agencies, according to the source, have different assessments of Russia's military power.
According to one assessment, Putin could take control of the entire Donetsk region by October, while according to another assessment, Russia faces a much more severe and inconclusive offensive.
According to Axios, the US sees three stages to achieving peace in the Russia-Ukraine war - a bilateral meeting with Putin to agree on steps towards peace, a bilateral meeting with Zelensky with the same goal, and a trilateral meeting with Putin and Zelensky to discuss the details.
The publication indicates that the final stage may not happen.
The Trump-Putin summit in Alaska took place on Friday, and after the meeting, officials provided very general information.
At the same time, publications are appearing abundantly in major Western media outlets, citing anonymous sources, about what was discussed at the summit, what Trump's subsequent conversation with Zelensky and European leaders was like, and what the prospects for achieving peace are in this context.