Pope was one of the standout performers for the Clarets during the 2021/22 season but was unable to prevent their relegation to the Championship on the final matchday of the season against his likely new club.
The England international kept nine clean sheets in 39 appearances for Burnley in all competitions, conceding 51 goals along the way.
Pope has been targeted by the Magpies as someone who can compete with Martin Dubravka for the role of first choice shot-stopper.
The custodian is set to undergo a medical on Thursday and the club could even complete the deal on the same day.
The goalkeeper most recently appeared for the Three Lions in a 3-0 friendly win over Ivory Coast at the end of March.
The 30-year-old looks set to continue in the Premier League but faces serious competition for a place in the England squad to travel to Qatar in late November.
After spending a major chunk of the first half of the season in the relegation zone, newly appointed manager Eddie Howe led the resurgence as the Magpies finished the season in 11th place, with one notable result being the 2-0 win over Champions League hopefuls Arsenal on the penultimate matchday.
