The Bogota side have won only two of the 12 Copa Mustang I matches and are 14th in the standings on 11 points.
Progression to the two-group semi-final stage is now unlikely as America, who are sitting in the eighth and last qualifying spot, have collected seven points more with six rounds remaining.
Carlos Robledo, a member of the board, revealed they decided Argentina-born Quintabani should step down and will make the recommendation to club president Juan Carlos Lopez.
Robledo told Futbolred.com: "We have made an unanimous decision in the executive committee. We are all together in this decision and the president will meet the coach to sort out everything about his departure.
"The party to get the benefit should be Millonarios. Each member of the committee may have their opinion, but we always maintain a union."
The board are also reported to be terminating the contracts of Argentinian midfielder Carlos Marinelli, formerly of Middlesbrough, Ecuadorian defender Ivan Hurtado and homegrown trio Miguel Rojas, Mauricio Casierra and Javier Araujo.
Quintabani had arrived at Millonarios in May 2008 to succeed Mario Vanemerak and interim coach Bonner Mosquera.