The Catalan giants are said to have been closely monitoring the 20-year-old since he made his senior debut for Liverpool Montevideo in February 2020.
Diaz, an academy graduate of the Primera Division side, has already established himself as a key player and has made a total 116 appearances across all competitions, scoring five goals and registering seven assists.
The deep-lying midfielder captained Uruguay's Under-20s at the South American Championship earlier this year, making eight appearances as La Celeste finished second behind winners Brazil.
Diaz is understood to have attracted interest from Brazil and Argentina, with Flamengo and River Plate both identifying the youngster as a possible target.
However, according to Mundo Deportivo, Barcelona are set to sign Diaz after reaching an agreement with both his representatives and Liverpool Montevideo.
The report adds that the midfielder's agent Martin Rodriguez Nader travelled to Barca's Ciutat Esportiva training complex to hold talks with chiefs of the Catalan club.
It is understood that Barca have agreed to sign Diaz for €8m and will initially integrate the youngster into the Barca Atletic side.
The report also states that the transfer of Diaz to Barcelona will depend on whether the La Liga leaders can avoid breaching Financial Fair Play regulations amid their well-documented financial concerns.
Barca boss Xavi is keen to reinforce his squad ahead of the 2023-24 campaign, targeting both ready-made players and talents for the future, but it remains to be seen whether they can afford to sign new players after La Liga chief Javier Tebas stated earlier this year that they must raise £177m before they can enter the market.
Another highly-rated youngster believed to be on Barcelona's radar is Brazilian striker Vitor Roque, who plies his trade with Athletico Paranaense and starred for Brazil at the Under-20 South American Championship.
However, the Catalan side will likely face stern competition from Premier League trio Manchester United, Chelsea and Arsenal for the 18-year-old's signature.
Barcelona have also been linked with a number of senior stars including Manchester City midfielder Ilkay Gundogan, while a swoop to re-sign legendary forward Lionel Messi - who will see his Paris Saint-Germain contract expire this summer - has also been mooted.