Manuel Agustín Fleitas Solich (30 December 1900 – 24 March 1984) was a Paraguayan football player and coach.

Fleitas Solich played for Club Nacional of Paraguay where he won two Paraguayan League titles, in 1924 and 1926.

He also played for Boca Juniors where as the captain of the team he led them to the 1930 Argentine title.

While playing for the Paraguay national football team, Solich had 32 caps and 6 goals.

In Europe, Solich coached Real Madrid for seven months of the 1959–1960 season, where he led the Spanish team to 21 wins, 5 draws and 4 losses.