Pope enjoyed an excellent 2017/18 campaign which earned him a place in Englands World Cup squad. However, a serious shoulder injury suffered last July saw Pope slip to third in the Burnley pecking order behind Tom Heaton and Joe Hart, with the goalkeeper failing to appear in the Premier League this season.
Nonetheless, the Daily Mail reports that Eddie Howe is keen to recruit Pope this summer. The Cherries are keen to secure a replacement for Asmir Begovic, who disappointed last campaign.
Bournemouth have also been tracking Stokes Jack Butland and considered offering Begovic to his former club as part of the deal. However, Pope represents a cheaper option and is now Howes number one choice.
Burnley are open to Pope leaving, with Tom Heaton now firmly established as Sean Dyches number one. Heaton has also overtaken Pope in the England pecking order and is part of Gareth Southgates preliminary squad for this summers Nations League finals.
The Clarets are also thought to be keen to move Joe Hart on following his poor form this season. Hart has been linked with newly promoted Norwich City and Championship club Blackburn Rovers in recent weeks.
Bouremouth have already been busy in the transfer window, securing the services of defender Lloyd Kelly from Bristol City in a £13m deal.
England under-21 international Kelly can play in the centre of defence and at left-back, and will provide cover for Charlie Daniels who is facing a lengthy spell out following knee surgery.
Eddie Howes side impressed in the early parts of the season but struggled with poor form in the second half of the campaign, eventually finishing 14th. The club kept ten clean sheets and conceded 70 goals throughout the course of the Premier League season, and Howe has made strengthening the defence a priority this summer.