South Bedfordshire District Council chief executive John Ruddock says there is a long way to go before Luton would be given permission for a new stadium.
The Hatters have located a site they are keen on by junction 12 of the M1.
Ruddock told BBC Three Counties Radio: "The club like the site and want to go there and we want to support them.
"The stadium was not going to be built in our area and it's a new proposal for us to consider. It's early days with lots of issues to be resolved."