The German club made a first offer of €11m for the 25-year-old, but Angers turned that down.
According to Sky Sport, Freiburg have now increased their bid to closer to the €15m asking price.
A final agreement between the two clubs should arrive in the next few days.
Santamaria has already said goodbye to his teammates at Angers in anticipation of his move to Freiburg.
Santamaria has attracted interest from Premier League clubs in the past year after his impressive performances.
The talented defensive midfielder has made 149 appearances for Angers since joining from Tours in 2016.