With Steven Gerrard suspended and vice-captain Frank Lampard troubled by a knee injury picked up on Chelsea duty at the weekend, Hodgson might be picking a team for the World Cup qualifier with San Marino without his captain and deputy.
Of the alternatives, Rooney and Hart are the most plausible candidates given Ashley Cole will not be considered, even if he does win his 99th cap.
Hart had plenty of backers when the job was up for grabs after John Terry was stripped of it for a second time last season - but he sees Rooney as a more obvious candidate.
"I've no idea who is going to be captain but I am pretty sure it will fall to Rooney," said Hart.
"He is our star man with 10 million caps at the age of whatever he is, 26?
"I imagine he is a little bit further up the queue than me."
Fabio Capello did give Rooney the job once, for the friendly defeat to Brazil in Qatar three years ago.
The Italian was never convinced by Rooney's leadership qualities though.
And as Dino Zoff and Iker Casillas have both captained World Cup-winning teams from their goalkeeping positions, there is no reason why Hart could not be considered.
"Of course I would, anyone would," said Hart, when asked if he would like to do the job.
"But I didn't go into goal thinking I wanted to be captain.
"I just want to play and do my best for the team, whether you've got the band or you haven't.
"It is a great thing to play for your country. I'm not really bothered who is in charge of it."
What moved Rooney to express his admiration for Hart on Twitter was his outstanding performance against Borussia Dortmund last Wednesday.
Hart made a succession of first-class saves to keep his side in the game, and the fact City emerged with a point stalled an early Champions League exit for the second season running.
It would be safe to assume he will receive no such accolades this week.
Rated as the joint worst team in the world by FIFA, it is hard to imagine San Marino posing any kind of threat.
"As a kid I used to enjoy it when we got hammered and there was loads to do," he said.
"But this is our livelihoods now. I want us to win 10-0 and me not to touch the ball. I am not going to stand there and sulk because they are not coming near the penalty area."
Although Hodgson has vowed not to take any risks with the players he needs for next Tuesday's crucial trip to Poland, there has been no suggestion Hart might be one of the players rested.
Indeed, he might want as much time as possible playing behind a defence no longer containing John Terry.
Hart laments Terry's absence, although diplomatically refused to enter into any discussions about the reasons for it.
Instead, he wants to keep focussed on his job, aware his own reputation is growing thanks to the observations of people like Rooney, to the point where he is being compared to the very best.
"Gianluigi Buffon was outstanding at the Euros and I've played against Casillas a few times. He's a ridiculously good keeper," said Hart.
"We've attracted (Hugo) Lloris to the Premier League now and he's also highly-rated, then there's Manuel Neuer, who seems to have that Germany jersey for a long time."
And, much closer to home, Hart even has words of praise for David de Gea, who has received so much criticism since his arrival at Manchester United.
"You have to find your own way of being a goalkeeper," said Hart.
"You don't have to be 6ft 8ins and able to fight 10 people at the same time.
"He (De Gea) has had great games where he's done things others couldn't do.
"There are pros and cons with every goalkeeper and the majority of the time, the pros outweigh the cons."