Henry is currently head coach of MLS side Montreal
The Cherries are looking for a new coach after they parted company with Jason Tindall, with Jonathan Woodgate currently in interim charge.
Henry has previously managed French side Monaco and worked with Roberto Martinez as a coach with the Belgium national side.
He has been in charge of MLS side Montreal Impact since November 2019 but it is believed that Bournemouth are keen to make Arsenal’s record goalscorer their new manager.
The 43-year-old made 123 international caps for France, scoring an incredible 51 goals.
He scored 228 goals in 376 appearances for Arsenal, with 176 of those goals coming in the Premier League.
The former Sky Sports pundit won two Premier League titles with Arsenal as well as two La Liga titles and one Champions League with Barcelona, where he played with Lionel Messi.
Bournemouth sacked Tindall after six months following four straight defeats.
A number of familiar names have been linked with the vacant role at the Cherries, including former Huddersfield manager David Wagner as well as Henry’s former Arsenal teammate Patrick Vieira.
However, it is believed that Henry could be in line for the post. The Frenchman would find a familiar face at Bournemouth, former Arsenal midfielder Jack Wilshere.
Current interim manager Woodgate is unbeaten since taking the role. But Bournemouth are looking to appoint an external candidate, after promoting Tindall from assistant manager to head coach failed to have a positive impact.
Tindall worked as Eddie Howe’s assistant as the club went from League Two to the Premier League.
However, relegation has meant a drop down to the Championship where Bournemouth currently lie in sixth place – 12 points adrift of Norwich City – and welcome Rotherham United to the Vitality Stadium on Wednesday night.