He said at an industry event that Britain's largest carmaker by volume would like to double production from 500,000 to one million cars a year.
But it would depend on the government helping to upgrade power supplies and invest in surrounding infrastructure.
The firm would also like a guarantee on access to engineering talent.
A company spokesman said the production target was "very much a want, rather than a will", but declined to commit on precise job numbers.
The 10,000 figure was mentioned by Lord Kumar Bhattacharyya, chairman of Warwick Manufacturing Group, which is part of Warwick University. Although it was not confirmed by the company, it was not dismissed either.
The carmaker's vision comes after the decision of Nissan to move two new next generation models to its Sunderland plant, backed by assurances from the government that it would help to invest in automotive research and development.
Nissan produced almost 477,000 vehicles in the UK last year, while just under 490,000 rolled off Jaguar Land Rover's (JLR) production lines, according to industry body the SMMT.
Now it seems JLR has thrown down the gauntlet to the government to match its ambition with big pledges for investment.
Specifically, the company is looking for help with infrastructure surrounding a 60 acre site and provide significant additional power resources.
Lord Bhattacharyya said he was sure "more than 10,000 jobs" would be created if JLR expanded to manufacture electric vehicles and batteries in Coventry.
He said the Business Secretary, Greg Clark, gave his assurances the government would look at the plans very seriously, because "in order to make the batteries and cars we need the power supply, which there is a shortage of in this area".
"There are challenges, but Coventry and Warwickshire is well placed to help make it happen, and I believe the timing is right," agreed Jonathan Browning, chairman of the region's Local Enterprise Partnership.
It is a tantalising vision of huge investment in the automotive heart of Britain.
Can the government match the soaring ambition of one of the UK's largest manufacturers with similarly ambitious support?
Although the company described this as an aspiration more than a plan, it is much more than day-dreaming.
According to company sources, this vision has been long held by JLR's boss, but he had chosen not to share it before and the Business Secretary was in the room to hear it.
The message was clear - the ball is now in the government's court.

The 18-year-old Manchester United supporter was watching at home in a village near Bingham, Nottinghamshire.
He felt the red card shown to the United winger was a crime so called police.
He later apologised for the call, saying he was caught up in the moment. Police will not take any action.
The fan, who has not been named, called police at about 21:20 GMT during United's second leg clash against the Spanish giants.
He was incensed by the referee's decision to show Nani the red card for a high challenge on Alvaro Arbeloa.
Ch Insp Ted Antill said: "While this recent example may be amusing, it illustrates the sort of insincere calls we have to deal with on a daily basis in the control room.
"They waste our time and they direct us away from genuine victims of crime, particularly if we dispatch officers out to something that turns out to be a bogus report."
He warned that prank 999 calls were a crime and said people had been prosecuted in the past.
"It's no joke. In this case, the man realised his bad judgement and apologised and we decided not to pursue it further," he added.
Nottinghamshire Police said it received 6,933 recorded hoax calls in 2012, which is about 2% of all reported incidents.
Had Tuesday's 999 caller followed Sir Alex Ferguson's example, he would have avoided a police telling off - the Manchester United manager was said afterwards to be "too distraught" to speak about the match.
The game turned after the dismissal of Portuguese winger Nani - whose real name is Luis Carlos Almeida da Cunha - with Real Madrid scoring two quick goals to win the match 2-1, knocking United out of the competition 3-2 on aggregate.
Jaguar Land Rover's chief executive Dr Ralf Speth has laid out a future vision which could see 10,000 new jobs created in the West Midlands.
[NEXT_CONCEPT]
A football fan was so disgusted with the referee's decision to send off Nani in Tuesday's Champions League clash with Real Madrid he called 999.