The 24-year-old, who is available on a free transfer after being released by AZ Alkmaar, had been set to sign earlier in the summer before suffering a knee injury while on trial during the Swans' tour of Holland.
However, Rodgers is hopeful that Agustien will sign on at the Liberty Stadium in the next week after overcoming the injury.
He told the club's official website: "Hopefully we'll get Kemy Agustien which will be done in the next week or so.
"He's coming on very, very well. Everything has been agreed in principle with him, subject to a medical, and we don't see that being a problem.
"We're looking forward to getting him in and getting him a part of what is already a very good squad."