"We will take at least 10-12 days to take a call on Shikhar's condition. We don't want to rule out a precious player like him," Bangar told the media on the eve of India's third World Cup clash against New Zealand.
Dhawan suffered the injury after being hit by a Pat Cummins delivery during his 109-ball 117 knock against Australia. While the X-ray didn't show any fracture, CT scan revealed otherwise and Dhawan was taken to a specialist for further assessment.
Pant, who was initially ignored for Dinesh Karthik when the 15-member squad was picked, has been named as his standby and is expected to fly in to England as cover.
India have won their first two matches against South Africa and Australia, respectively. India will next face New Zealand at Trent Bridge on Thursday.
Dhawan will be monitored in the team camp for 10 or 12 days. Bangar also challenged Rahul to make the opportunity count as the team aims to compensate for the absence of Dhawan at the top of the order.
Rahul will open the batting for the foreseeable future and Bangar tasked the 27-year-old with adapting quickly.
"As far as the batting order goes, KL moves up at the top of the order," said Bangar.
"The advantages of playing in various situations is that you understand the game a lot better. If you are batting in the middle order and suddenly you go and bat in the top order, you know how challenging it can be, wherein you need to negotiate two new balls but you also understand that there are these boundary opportunities.
"So if a player is able to do that, it helps the team big time. So it's a mental adjustment, and any player who is able to do that requires a lot of skill, but ultimately it will enhance the position that he will bat in, and it will help the team's cause," Bangar said.
Rahul is no stranger to opening the batting, but the last time he did so was in January 2017.
He opened in each of his first six ODIs -- against Zimbabwe and England -- but was earmarked as the solution at number four after a warm-up century against Bangladesh in Cardiff.
India's approach to the first powerplay since the 2015 World Cup has been conservative, with no side scoring slower than their 3.5 runs per over in the tournament thus far.
Despite Dhawan's absence, it seems their approach won't waver as Bangar encouraged Rahul to continue to show caution, starting against New Zealand at Trent Bridge on Thursday.
"The batsmen have to be a bit circumspect when the conditions are cloudy and there are two new balls. You always want your top bowler to show discipline and put the team in a great position because if you're in a good spot at the end of 10 or 15 overs, the seam tends to soften up.
"From that point of view, it's always a good strategy. Every opening batsman would like to have that sort of strategy, where if the conditions are challenging, you always want to give the bowlers the respect at times," Bangar said.