Marca says the pair have returned to full training after overcoming injuries.
Umtiti has endured an injury-ravaged 18 months and his problems continued last month when he sustained a calf injury on his return to individual training.
Fati's injury was considered less serious with the precocious 17-year-old having felt some discomfort in his knee, according to reports.
Barcelona erred on the side of caution with the forward but he is now able to train with the first-team again.
The news will be a welcome double boost to Barcelona manager Quique Setien.