Savic was part of the Montenegro side that drew with England last year
Partizan Belgrade centre-back Stefan Savic is undergoing a medical at Manchester City, BBC Sport understands.
The 20-year-old would become City’s second defensive signing of the summer after Monday’s deal for Gael Clichy.
The Montenegro international had a 10-day trial with Arsenal last year.
BBC Sport’s Phil McNulty said on social networking site Twitter: “Man City’s main business today is concluding the deal for Partizan Belgrade defender Stefan Savic.”
The Eastlands outfit would also need to secure a work permit to complete the deal.
Savic was a member of the Montenegro side that frustrated England in a 0-0 draw at Wembley in October 2010 in a Euro 2012 qualifier.
He also faced English opposition when turning out for Partizan against Arsenal in the Champions League in December.
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Savic undergoes Man City medical