Eddie Howe is looking for reinforcements up front with Callum Wilson out injured and his side lacking goals this season.
The Telegraph reported that Newcastle United have approached Burnley for the striker and are pushing hard to secure the signing.
Crucially, the player is also keen on moving to Tyneside and the club have not been discouraged so far in their pursuit for the New Zealand striker.
Should a move for Wood not materialise, Howe has other options in mind with the report stating that Arsenal's Eddie Nketiah and Liverpool's Divock Origi also being considered.
Signing the former though may prove problematic as the Gunners are still looking to tie the 22-year-old down to a new long-term contract.
Liverpool meanwhile are light of forward options at the moment with Sadio Mane and Mohamed Salah both at the Africa Cup of Nations.
Outside of the Premier League, the club are also looking at Zenit St Petersburg striker Sardar Azmoun and Marseille forward Bamba Dieng.
One thing that is for certain is that the club want to bring in a striker and centre-back before their crucial match against fellow strugglers Watford in the Premier League.
Kieran Trippier recently became the first signing in the new era and the club are also keen on Lille centre-back Sven Botman and Sevilla's Diego Carlos with the latter already the subject of an unsuccessful £25milllion bid from the Geordies.