The Sun says Dyche is ready to make a low £1.5m bid for Lennon, 30.
Dyche missed out on Lennon in the summer — having tried to sign him in August.
Lennon's deal runs out in the summer and there is no sign of him staying.
“We'd both like that, it's an ambition, but we don't take too much notice of what goes on, it either happens or it doesn't," he said.
“It's something we both want, and it's a case of keep playing well, keep doing what we can, and if it doesn't happen, keep playing well for your club and doing well, and seeing how far we can take this club forward."