Talks have been held with Pope.
Eddie Howe would have an alternative to Martin Dubravka with the 30-year-old England international.
Part of a £65m loan is due to be paid back because of the club's failure to stay in the top flight.
Pope was named in the Nations League squad despite not having played for England in over two years.
He had hopes that he could make the World Cup in November.
Eddie Howe has been trying to improve his side since the takeover.
Dubravka came back from a foot injury to make 26 appearances for the club last season as they moved up from the bottom of the table.
Lille's 22-year-old centre-back Sven Botman is one of the players Howe's side are attempting to sign.
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