UPDATE 1-Canada's PM optimistic on NAFTA as deal on autos appears closer

(Adds quotes, details, background)

OTTAWA, March 21 (Reuters) - Prime Minister Justin Trudeau said on Wednesday he remained optimistic Canada would get a good deal at the NAFTA modernization talks amid signs negotiators could be closer to settling one of the trade pact's most contentious issues.

Officials are due to meet next month for the eighth round of talks, which have bogged down as Canada and Mexico try to digest far-reaching U.S. demands for changes to the $1.2 trillion North American Free Trade Agreement.

People close to the process say the U.S. side, citing the need to finish before Mexican presidential elections in July, is now showing more flexibility.

"We continue to be optimistic about our capacity to get to a good win-win-win (deal)," Trudeau told reporters.

Toronto's Globe and Mail newspaper said the U.S. side had dropped its insistence that all autos made in NAFTA nations should have 50 percent U.S. content. Canada and Mexico had rejected the demand.

The news helped boost the Canadian dollar to a six-day high against its U.S. counterpart while Mexico's peso firmed more than 1 percent.

A spokesman for Canadian Foreign Minister Chrystia Freeland said he could not comment.

A Canadian source briefed on the talks said "there appears to have been positive progress made on certain key issues" involving autos. The source gave no precise details.

David MacNaughton, Canada's ambassador to the United States, told reporters on Tuesday there had been movement on the autos issue but stopped short of saying the U.S. side had dropped its content demand.

"They came back with some ideas that - if you take them to their logical conclusion - would mean that you wouldn't need that requirement," he said.

"Did we get to somewhere where you could shake hands and say, 'We've got a deal? Absolutely not ...Whether or not we can get there I don't know," he added.

MacNaughton's quotes were reported by the Canadian Press. A Canadian official confirmed their accuracy.

Mexico's economy minister last week said that if the three nations did not finish the talks by the end of April, the process would drag on at least until the end of 2018.

Mexico's presidential vote is on July 1 while U.S. congressional elections are set for November.

"We are very aware of the time pressures in both the United States and Mexico regarding the mid-terms and regarding the Mexican elections, and we are there working very, very hard," Trudeau said. (Reporting by David Ljunggren Writing by Andrea Hopkins Editing by Bernadette Baum and Paul Simao)