The Miami Herald reported Harris and Spence were ruled ineligible by the school, which has asked the NCAA to start the reinstatement process.
The reported ruling comes in the wake of a review by the university of the eligibility of 15 current student-athletes due to potential violations.
The Herald reported at least four other football players were not declared ineligible because the impermissible benefits each allegedly received from former Miami booster Nevin Shapiro were less than $100. That money can be paid back usually by donating to a charity, according to the report.
Earlier this week, a Yahoo! Sports report detailing Shapiro's gifts to Miami athletes said he provided improper benefits to at least 12 current Hurricanes football players.
Shapiro is currently in prison after being sentenced to 20 years for his role in a $930 million Ponzi scheme.
Other players who may have violated rules, according to the Yahoo! Sports report, are Vaughn Telemaque, Ray-Ray Armstrong, Travis Benjamin, Aldarius Johnson, Marcus Forston, Olivier Vernon, Marcus Robinson, Adewale Ojomo, Dyron Dye and JoJo Nicholas.
The Hurricanes, who start the season September 5 against Maryland, had to declare the players named in the Herald report ineligible. This way, the NCAA can review each player's case for possible reinstatement or determine how long they will be out before the season opener.
Miami offered, and was granted, the chance to conduct a joint investigation with the NCAA. On Monday, university president Donna Shalala pointed to the cooperation of football coach Al Golden, who was hired in December to replace Randy Shannon, and basketball coach Jim Larranaga.
In addition to the football players who were said in the Yahoo! Sports report to have accepted improper benefits, Shapiro also claimed he paid $10,000 to secure the commitment of basketball player DeQuan Jones.
Among the other names disclosed were former Hurricane football stars Devin Hester, Antrel Rolle and Jon Beason. The report also said some former coaches had direct knowledge of the players' involvement, including former men's basketball coach Frank Haith.