The former Bournemouth boss, 43, has held discussions with members of the club's board, including major shareholder Dermot Desmond, reports BBC Sport.
Howe left Bournemouth in August 2020 when the club's five-year stay in the Premier League came to an end.
He has been linked with Sheffield United and Newcastle in recent weeks.
Howe was in charge at the Vitality Stadium for more than 450 games across two spells spanning more than a decade, guiding them to three promotions in six seasons and taking them from League Two to as high as ninth in the Premier League.
He also had a stint with Burnley in the Championship from January 2011 to October 2012.