The 21-year-old was not part of Leganes preparations but two cases of Covid-19 and Javi Rubio's physical problems have made Garitano summon him at the last minute.
The Ghanaian, who was on loan at UD San Sebastián de los Reyes, has been recalled by his parent club.
He has started training with the side after the situation changed due to Covid-19.
The midfielder had an outstanding season with San Sebastien, helping the club gain promotion to the Primeira Division RFEF.
Ofoli Quaye played 24 games last season, starting 23 and scoring to goals for the third tier club to draw interests from top team in Spain.