Speaking with CarAdvice at the 2015 New York auto show, Callum said he personally has a huge desire to take the Jaguar brand to new places, where the likes of Mercedes-Benz (with its A-Class), BMW (1 Series) and Audi (A3) have seen such dramatic levels of success.
"We want to grow our family," Callum said, before indicating that it's hard to ignore the potential income that a model smaller than the recently-revealed XE (pictured below) could bring.
"There’s always space to go smaller – the world is changing very quickly," he said.
"My personal belief, and I must emphasise that, is there is space to go smaller. I am a great lover of small cars, to the point I even own a Mini."
However, the fact Jaguar would likely have to develop such a model upon a new architecture, or borrow and adapt one from parent company Tata Motors, means the project is hard to nail down.
"I think there’s a huge opportunity in the small car market, but it’s a very difficult business," Callum said. "It’s hugely competitive, it’s hugely price-conscious. And you know we’re too small at the moment to think about taking on that sense of volume and competitive price.
The current aluminium-intensive architecture that underpins the new XF, XE and upcoming F-Pace has a rear-wheel drive bias and its balance is such that it would be impossible to spin-off a smaller model. On top of that, Callum said a rear-drive small car would be compromised in its packaging, so front-drive would be the way to go.
"I am at the conclusion that if we were to go smaller than XE we would have to go front-wheel drive so that we can get size out of the car. And I think the world will accept that. BMW is accepting it," he said.
"So that’s fine, front-wheel drive cars are fine. The technology now kind of compensates for its misgivings," he said.
However, despite having obviously thought about it a lot, Callum reiterated that at this point there are no firm plans for a smaller model to make it to production anytime soon.
"There’s no plan to do anything – clearly we think about it, we investigate it. But it’s a very difficult business," he said.
"You have to take a very big brave pill to go in to that marketplace."
Tell us what you think below - should Jaguar take the brave pill and build a new smaller model?