New Zealander Jack joined the London club in 2007
Saracens have told 15 of their playing staff they will not be required next season as they will be replaced largely by South African players.
Former All Black Chris Jack is the highest-profile casualty, along with Cencus Johnston and long-standing club men Kevin Sorrell and Ben Skirving.
Ex-Springbok Brendan Venter will become head coach at the end of the season.
Venter told the 15 players the news on Monday, and the players are thought to be considering their response.
In a statement, the London club said: "It would be completely inappropriate for the club to make any specific comment on these private meetings."
It went on: "Many of the players were enthused and excited by what they heard; inevitably, some were disappointed."
Saracens are now effectively run by a group of South African investors who also have a stake in provincial sides the Sharks and the Stormers in their home country.
It is thought that players from those two sides could well be brought in at Saracens.
The Stormers have revealed that some of their players have already been approached by Saracens.
"Some of the players have told us that they have been approached by Brendan (Venter)," Stormers media manager Frikki Erasmus said.
"(One of) the players that has mentioned this approach is Schalk Burger. There have also been indications that Jean de Villiers has been approached, and Schalk Brits."
Saracens' statement added: "The club is already working with the various players' agents and the PRA [Professional Rugby Players' Association] to assist in securing their futures, and, without exception, the club will act decently and honestly.
"This has been a difficult week, but the reality is that Saracens is not immune to the economic realities being faced by many companies across the country."