His remarks followed a Wednesday night call between Mr Trump and Mexican President Enrique Pena Nieto in which the leaders discussed the renegotiation of the North American Free Trade Agreement (NAFTA).
Mr Videgaray said the call, which was initiated by Pena Nieto and lasted about 20 minutes, focused exclusively on the looming talks over NAFTA's "renegotiation and modernization." He noted that Mr Trump wanted to see the talks accelerated.
"We have generated a respectful dynamic through dialogue ... we've advanced enormously in the correct direction," Mr Videgaray told local broadcaster Televisa in an interview.
He added that the two leaders did not set a date for a summit.
Mr Videgaray struck an optimistic tone despite noting that the US and Mexican governments still had "many well-known public differences."
"I believe that all the conditions to reach a good negotiation exist, that will suit Mexico ... and that is also good for the region, for both Canada and the United States," said Mr Videgaray, who previously served as finance minister.
Mr Trump said earlier on Thursday morning on Twitter that renegotiating NAFTA with neighboring Mexico and Canada was "very possible," but he threatened to scrap the pact if the countries failed to reach a "fair deal for all."
(Reporting by Veronica Gomez and David Alire Garcia, Editing by Chizu Nomiyama and W Simon)