Kohli scored a tournament-best 765 runs during the recent World Cup.
Shan Masood has been announced by the PCB as the new Test captain while Shaheen Afridi will be the T20 captain.
Babar sought to steer clear of any speculation and said his focus was solely on finishing their group stage on a winning note at the Eden Gardens.
Babar is approaching the tournament's most-anticipated clash at the Narendra Modi Stadium, the world's largest cricket venue, with a complete disregard for the past.
Mohammad Rizwan scored an unbeaten 131 to help Pakistan record a six-wicket win.
Shaheen Shah Afridi also lauded the Indians for their warm reception for the Pakistani cricketers.
A heated argument erupted after Pakistan's last-ball defeat to Sri Lanka in the Asia Cup.
Babar led from the front with a masterly 151 and Iftikhar Ahmed produced an unbeaten 109 in their opening game of the Asia Cup against Nepal.
An exhibition match of the Pakistan Super League at the Nawab Akbar Bugti Stadium, Quetta, was halted for some time following an explosion in the Police Lines area, which left five people injured.
Babar was the only player to breach the 2,000-run mark during the calendar year across all formats, and he did it in style as he broke past that milestone while amassing a whopping 2,598 runs at an imposing average of 54.12.