Members of the British Racing Drivers' Club (BRDC), which owns the Formula One circuit and surrounding land, last month gave their board a mandate to negotiate with the carmaker.
Jaguar Land Rover hopes to boost its brand by building a hotel and visitor centre at Silverstone, allowing tourists and families to visit and drive vehicles on the track, a source told Reuters.
JLR has said it was "exploring potential options" but discussions remained confidential.
Allen, on a visit to the Spanish Grand Prix circuit for this weekend's fifth race of the season, told Reuters there was an exclusivity agreement in place until June 30.
"But that does not necessarily mean you have to do a deal by then," added Allen, who runs the operational side of the circuit but is not part of the negotiating team.
"I am sure that the board have the best interests of the circuit and the BRDC at heart. They will take as long as they need to get to a deal if a deal is to be done. It’s not guaranteed."
Allen said the BRDC would remain 100 percent owners of the Silverstone Circuits business and continue to run the British Grand Prix whatever the outcome.
"The business will carry on whether the assets are sold or not," he said. "We want to diversify into a leisure and entertainment venue. A destination venue, whether that’s concerts or car shows."
Access to the track would be more limited, however, and Allen indicated that formed a big part of the talks.
He said the BRDC wanted a stronger financial platform for the business, with a capital injection also securing jobs, while JLR would benefit by association with a track that has hosted Formula One since 1950.
"They see the synergy of the two brands as a great relationship and it works for both parties," he said.
Allen said Silverstone had made a pre-tax profit of 1.5 million pounds ($2.16 million) last year, after losing 4.5 million in 2014, but a capital injection could take that to 5 or 6 million, "which is where it should be."
A race day crowd of 150,000 is expected at the British Grand Prix in July.
(Additional reporting by Costas Pitas, editing by Peter Rutherford)
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