Vucic said he will discuss the issue with the representatives of parliamentary parties before making the decision. In Serbia, the president nominates a prime minister-designate who then needs parliamentary approval.
The populist Vucic is widely expected to appoint a loyalist and maintain control of the government even as he moves into the largely ceremonial presidential position. His Serbian Progressive Party holds the majority in Serbia's 250- member parliament.
A former extreme nationalist who now says he wants Serbia to join the European Union, Vucic was sworn in as president Wednesday after sweeping the election in April.
In his speech on Wednesday, Vucic said he wants to boost Serbia's defenses, while staying out of any military alliance. He also has been strengthening ties with Serbia's traditional ally, Russia, which has agreed to supply fighter jets and battle tanks.
Opposition groups accuse Vucic of imposing an autocratic rule.