Tevez announced his retirement from football earlier this month, having not played since leaving Boca Juniors in the summer of 2021.
Rosario Central find themselves in mid-table three games into the Argentina season.
Vice-president Ricardo Carloni told TyC Sports: "The board accepted a proposal put forward by Tevez's staff, and we are now moving forward with the negotiations.
"We will discuss it this weekend. The proposal was approved by the board. The idea is that if all goes well, we could have him by Tuesday."
Rosario's players are already relishing the prospect of playing under one of Argentina's best players of his generation, with goalkeeper Gaspar Servio telling TNT Sports: "For me, it's something special that Carlitos [Tevez] can come here.
"If he does come here, the group will back him to the death. I hope he comes. He has a lot of experience as a player, and we are all ready to learn and to help Central."
Tevez retired with a record of 308 goals in 746 club games, having also turned out for the likes of Brazilian side Corinthians, West Ham United, Manchester United, Manchester City, Juventus and Shanghai Shenhua.
The 38-year-old won two Premier League titles and the UEFA Champions League with Manchester United before making a controversial switch to Manchester City, where he won another top flight title.
A move to Juventus in Italy brought two Serie A titles for Tevez.
Tevez won 76 caps for Argentina, scoring 13 goals and played at the 2006 and 2010 FIFA World Cups.
