The C-X17 concept was on show in LA
Although not officially confirmed for production, the C-X17's design and packaging "was feasible for manufacturing".
"We don't do concepts that overpromise," said Callum. "It is looking good. Although I can't confirm it for production, my personal view is that we should do it."
Callum has been pleased with reaction to the C-X17 since its reveal at the Frankfurt motor show in September and subsequent launches in shows in Dubai and Los Angeles.
"I had originally planned a speech with a defensive state of mind, saying we do have the right to do a car like this if we follow Jaguar values," said Callum.
"But I didn't need to use it as the world loves it. There has been no real dissenting voice, people are saying now its about time we joined the segment.
"It has been very well accepted. If we do it, it has to be a sports crossover, a driver's car, a performance car. It has to turn heads."