The 24-year-old was released by Oxford United at the end of last season after being deemed surplus to requirements by manager Michael Appleton.
This was despite the forward scoring seven goals in 17 league appearances for the U's, which helped them to promotion to League One.
Bowery, now a free agent, is said to be on the radar of several clubs, including the Magpies, according to the Nottingham Post.
The Nottingham-born footballer played under current Notts boss John Sheridan at Chesterfield.
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