The 28-year-old's loan deal from Stoke City expires at the end of the season, but he would be eager to remain with the Clarets as they prepare to make a return to the Premier League.
"I don't know what's happening at the moment but I would love to join Burnley," Kightly told the Southend Echo.
"Since I've been here I've not spoken to anyone from Stoke so I think that shows I won't be there next season.
"Winning promotion here is up there with the best moments I've had in my career so of course I would like to stay and help them in the Premier League."
Kightly is expected to be involved against Ipswich Town on Saturday afternoon.