Palace legend Freedman, 36, enjoyed 10 years at Selhurst Park over two spells in his playing days, during which time he made over 350 appearances and scored more than 100 goals.
Following the sacking of George Burley on New Year's Day, Freedman took caretaker charge of Monday's 1-0 home win over Preston.
Despite the victory the Eagles remain in the Championship's bottom three and in need of the right man to guide them up the table, with experienced second tier bosses Steve Coppell and Paolo Sousa linked to the role. But Ambrose believes rookie manager Freedman is a contender.
He told the South London Press: "Dougie's come in and brought his own message to the team. There would be no surprise in the camp if Dougie was appointed manager - he has got a lot of respect from the lads."