Umtiti has made 83 appearances for the club in all competitions since arriving from Lyon in 2016, scoring twice.
The 24-year-old featured and scored in Friday's worldwide friendly win for France over Italy.
His talents have not gone unnoticed, with United boss Jose Mourinho an apparent admirer and was reportedly interested in bringing him to Old Trafford this summer.
After Manchester City and Liverpool spent big on defenders Aymeric Laporte and Virgil van Dijk, respectively, in January, Manchester United were linked with a move for Umtiti. But, they have now received a setback in their bid to sign Umtiti, with the Frenchman reaching an agreement with Barcelona over a new five-year deal.
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But Ramsey, speaking after Wales' 0-0 draw against Mexico in California, gave his backing to Emery, the former Sevilla and Paris Saint-Germain manager.
Last season, Barcelona won La Liga conceding just 29 goals in 38 games, with Umtiti playing 25 times after fighting with injury problems.
He will officially put pen to paper on Monday, which will delight Barcelona fans as he was one of the few key first-team players who were yet to sign new deals.
Umtiti will then give a brief press conference at theRicard Maxenchs press room at 10:30am before rejoining the France squad for their World Cup preparations.