The Gunners graduate has been a fringe player under manager Mikel Arteta this term and he has made just one start.
Eddie Howe's side bolstered their squad over the summer, but they are planning a mid-season spending spree too.
They are unlikely to meet the Gunners' £50 million asking price for Smith Rowe, but could propose a different solution.
The Tyneside outfit could make an initial loan approach for the 23-year-old with an option to buy at the end of the season.
If Smith Rowe were to leave Arsenal, the club are likely to pursue a suitable replacement with Premier League experience.
Wolverhampton Wanderers' Pedro Neto could be a realistic target. Arteta has been his admirer since his breakthrough at Braga.
