It wasn't always like that during the promotional gig — they did share some laughs — but the somewhat awkward vibe captured in a few snaps may be because both Morgan and Kohli are in charge of teams expected to bring home silverware.
England is ranked No. 1 in the world in ODI cricket and is a hot favourite to win its first World Cup while India is ranked second and boasts matchwinners with both bat and ball.
If those two teams play to their potential, it won't matter how well Kane Williamson or Martin Guptill perform because on their day, an in-form India and England can outgun anyone in the 50-over format.
Morgan and Kohli know that, and perhaps that's why small talk was at times kept to a minimum at yesterday's press conference. They've already got a steely edge about them and buddying up to their biggest rival a week before the tournament starts won't help them when they need a killer instinct in the the World Cup.
If England and India — and their captains — are already laser focused and hellbent on making sure nothing gets in the way of winning, then Australia has reason to be scared.
England's batting firepower is its greatest strength. Morgan, Jason Roy and Jonny Bairstow can all clear the ropes with ease and Jos Buttler's game was hailed recently by Ricky Ponting as "out of this world". Throw in Ben Stokes and Moeen Ali lower down the order and scores of 350-plus — taking into consideration smaller English grounds — may be the norm.
In a column for The Daily Mail, former England skipper Nasser Hussain said: "This is not only the best World Cup squad England have ever had, it's probably their best ever one-day squad.
"If I was captaining against this England team, I would be fearful because so many of these players can destroy you."
India too has plenty of star power with the bat. Kohli, averaging nearly 60 in ODIs with 41 tons, is the best one-day batter in the world and Rohit Sharma is the only player to have three ODI double centuries to his name.
Bowling-wise, paceman Jasprit Bumrah is in a league of his own and the cool head of MS Dhoni will be crucial in pressure moments.
While far from alone, the Black Caps' preparation for this this pinnacle tournament could hardly be described as ideal.
Williamson's men have not played an ODI for three months – their last match in this format an 88 run win over Bangladesh in Dunedin back in February.
Since then nine World Cup members played various roles in the Indian Premier League and four others featured in the three-match series against a near full-strength Australian XI earlier this month.
After such extended time apart, pressure is on to immediately combine.
"Having a tournament on the other side of the world where it's a different season and our domestic competition isn't going on is the nature of the beast," Williamson said.
"To a degree that's the nature of the international game where it's constantly evolving and you're changing formats all the time.
"It's a big tournament on the calendar and preparation has been different for each team.
"There is that individual component but you want to see the team come together as a collective and that's the best way to build momentum into the tournament. That's what every team will be looking to do.