[1] Because Udinese ran out of non-EU registration quota for international signing (which Udinese had to buy one from other club) as well as the performance of Slovenian internationals Samir Handanović, Brkić was signed by Serie A club Siena[2][3] in definitive deal[4] from Vojvodina, which he would transfer back to Udine in a later time.

In a 1–1 draw against Bologna on 25 April 2012, Brkić scored an own goal from an Alessandro Diamanti free kick, denying Siena a win.

[11] Having established himself in the first team, Brkić made his debut for the club in the UEFA Champions League qualification round against Portuguese side Braga.

However, the next game was even went worse for Brkić when he gave away the penalty in early minutes and received a red card in a 4–1 loss against regaining champion Juventus.

On 4 October 2012, Brkić was in goal when Udinese beat Liverpool 3–2, making good save from Luis Suárez twice and a header from Jonjo Shelvey.

Brkić's performance with Udinese were praised in the media, who noted that he "saved at least three goal-bound efforts while blocking several strong shots and commanded his area giving sustenance and substance to his whole defence".

Brkić, who had already agreed terms with PAOK's president/technical director Ľuboš Micheľ, passed his medical at the Thessaloniki-based club and then signed his new contract, leaving Italy after five consecutive seasons.

Brkić, along with the experienced Greek internationals Panagiotis Glykos and Markos Vellidis, is expected to be part of a very strong triplete in goalkeeper's position for PAOK ahead of 2016–17 season.

[22][23] Brkić started participating in the national team, playing for Serbia U-21 and was even in the U21 squad for the 2009 UEFA European Under-21 Football Championship despite being age twenty-two.

[26] Years on, Brkić was the national first choice goalkeeper, beating competition from Vladimir Stojković in the World Cup qualifier.