The newspaper reports (on page 74 of its Saturday, 27 July edition) that the 58-year-old is ready to return to another of his former clubs, Hull City, with a £10 million offer for Bowen.
It was Bruce - who left Sheffield Wednesday to take on the role at his boyhood club, Newcastle, 10 days ago - that signed the Hull winger for the club's Under-23s.
But it wasn't until after Bruce's 2016 departure, when he had long since joined Aston Villa, that Bowen emerged in the Tigers' first team.
Since then, the 22-year-old has scored or made 45 goals - two against Aston Villa - in 99 games.
And according to the Daily Mirror, Hull would struggle to keep him should an offer close to his £12m valuation arrive from Newcastle, or any other club.
The newspaper claims Bruce has placed Bowen at the top of his transfer wishlist, along with the OGC Nice winger, Allan Saint-Maximin.
Aston Villa - who will join Newcastle back in the Premier League this forthcoming campaign - have signed up Anwar El Ghazi, Jota Peleteiro and Mahmoud 'Trézéguet' Hassan in Bowen's position since their promotion in May.
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