Gary Sweet said talks have started with Luton Council, which bought the stadium in 1989.
Writing in the club's programme, he said: "We have a strong desire to put the ownership of Kenilworth Road back into the hands of the club."
He also said neither the future redevelopment of the ground or the club's relocation could be ruled out.
Mr Sweet revealed his plans for the club in Saturday's programme notes to update what he called the "faithful support".
Citing the club's "23 heroic supporters" whose delayed coach journey to Grimsby for last Tuesday night's fixture saw them arrive at the ground to find the Hatters already three goals down, he said the directors "thrived on such committed support" and it was this drove them on to achieve a stable club.
He said either option to achieve this "stability", would take a while to become a reality and due to "commercial delicacy" any plans would not yet be made public.
"Realistically, given current market conditions, any such plans would take a number of years to reach fruition," he said.
"These [plans] would also be dependent upon one location delivering a long term formula to support the club's sustainability."
Mr Sweet also stated he was aware short-term improvements to the ground would be needed.
"We are assessing plans to enable us to increase our capacity, and to modernise a part, or parts, of the stadium," he wrote.
Luton Borough Council said that as a landlord it was in discussions with the club about "a number of issues".
"Within those discussions, the club has identified as one of many options, the possibility that they may be interested in buying the freehold of the site at a point in the future," a statement read.
"Currently the site is not on the disposal list and does not have a purchase value attached to it."
Mark Chapman, from the supporters club, said buying back the ground would be "progress in the right direction" if the club had aspirations to get back to "at least" Championship football.
"It then gives them an asset that they can then use to raise finance if they are to move," he said.
"The existing facility, as much as we love it, is antiquated and I personally can't see that there is any way they could build it up to a capacity of 20,000 on the current site."
Luton Town FC have begun talks to buy back its ground, the managing director has confirmed.