Sunderland are desperate for reinforcements and could be aided in their pursuit of Walters.
The 34-year-old has recently returned from an injury which has seen him miss most of the season, but the Black Cats want the former Stoke City man to replace Lewis Grabban.
Walters would join a few familiar faces if he is to move to the Stadium of Light. The striker has played 51 times for the Republic of Ireland alongside the likes of John O'Shea, Darron Gibson, Marc Wilson and Aiden McGeady.
The Irish contingent at Sunderland have enjoyed success with the national team, qualifying for two European Championships and reaching the last 16 at Euro 2016.
Playing with teammates that he knows and trusts will be a big factor for Walters and he could particularly link up well with McGeady, having done so on many occasions for Ireland.
He should not need too much time to settle in with all that in mind, so he would be in a good position to arrive and hit the ground running, which Sunderland will desperately need him to do.
Walters has played just five times in all competitions for Burnley but previously scored 62 goals over seven seasons for Stoke. The deal could be confirmed in the coming days.