The 34-year-old is on Sunderland’s radar with Chris Coleman desperate to bolster his attacking options.
Following the departures of Lewis Grabban and James Vaughan this month, Sunderland currently only have teenage forwards Josh Maja and Joel Asoro to call upon.
Walters, a £3million summer signing from Stoke City, is one of a number of forwards on Coleman’s wanted list but the Black Cats will have to be patient.
A knee injury has seen Walters’ opportunities limited, with the Republic of Ireland international playing just 37 minutes of Premier League football for the Clarets so far this season.
He was an unused sub at the weekend.
When asked if Walters was Sunderland-bound, Dyche told the Lancashire Telegraph: “Not at the moment.”
Asked if the move could happen later in the window, Dyche added: “We’ll see.”
It is understood the return to fitness of striker Chris Wood could allow Walters to move out on loan later this month.
Coleman has also been credited with an interest in promising Manchester City striker Lukas Nmecha.