The Dane is a free agent after the Gunners opted not to offer him a new deal at the Emirates.
Newcastle are looking to recruit heavily in the transfer market this summer having lost strikers Luuk de Jong, Loic Remy and Shola Ameobi.
Remy and De Jong returned to Queens Park Rangers and Borussia Monchengladbach respectively, following the end of their loan spells, while Ameobi has been released.
Bendtner only made eight appearances last term, as Olivier Giroud continually led the line in a lone frontman role for the majority of the season.
According to the report, the 26-year-old earns around £52,000-a-week, and Newcastle are prepared to offer him around £12,000 less.
A two-year contract is said to be on the table for Bendtner who is attracting attention from elsewhere in the Premier League.
Bendnter is also reportedly the subject of interest from newly-promoted Burnley, who are looking to add Premier League experience and some competition to Sam Vokes and Danny Ings.
Hull City are another club who have been linked with a move, with Steve Bruce looking to beef-up his striking ranks following the January captures of Nikica Jelavic and Shane Long.
Bendtner's exit was long in the making at Arsenal. The Gunners loaned the player to the likes of Birmingham City, Sunderland and even Serie A giants Juventus, but none were keen to make the deal permanent.