After first fixture and lose against Napredak Kruševac, Mladen Dodić decided to give Rajković a chance, because of his merits in winning 2013 UEFA European Under-19 Championship.

[14] After Bajković's and Vesić's departures, Rajković stayed with a year younger Filip Manojlović and Marko Trkulja who returned from Spartak Subotica, where he was on loan.

After Milijaš's departure, Mijailović's suspension, Luković's injury, and Lazović's conflict with management, coach Nenad Lalatović decided to give the captain's armband to Rajković.

[16] On 29 June 2015, Rajković signed a new three-year contract with Red Star, after days of speculation about his potential transfer away from the club.

The Crvena zvezda captain was also a top target for Paris Saint Germain along with Kevin Trapp, who signed for Les Parisiens at the end.

[18] After great saves in first rounds of the Serbian SuperLiga, despite Zvezda's poor start, Turkish champion Galatasaray declared interest in him.

Predrag Rajković was one of the contestants at 2018 FIFA World Cup qualifying draw, which took place at the Konstantinovsky Palace in Strelna, Saint Petersburg on 25 July 2015.

Rajković made an assist to Viðar Örn Kjartansson in the State Cup match against Hapoel Bnei Lod played on 7 January 2017, saving a shot from the opponent's previous attack.

[23] On 14 December 2017, Rajković won the Toto Cup trophy with Maccabi, beating Hapoel Be'er Sheva in final match of the competition.

Mendy had been hugely impressive in his first season in Ligue 1, keeping 14 clean sheets bettered only by Lyon's Anthony Lopes and Nice's Walter Benitez.

[29] Rajković was one of the most deserving players for winning the 2013 UEFA European Under-19 Championship, when he saved goal many times with great interventions and stopped penalties.

[32] In the final, Rajković was one of the most important men on the field, keeping the result with incredible saves, being awarded the best goalkeeper in the competition.