The Danish striker is deemed surplus to requirements by Arsene Wenger at the Emirates and Stoke manager Tony Pulis is understood to be keen on taking the 23-year-old to the Britannia Stadium, according to The Mirror.
Bendtner has been linked with a move away from Arsenal for much of the summer and his agents began discussions over a potential move with Pulis at the weekend.
"We are threadbare at the moment," Pulis said. "Fingers crossed we can bring in one or two players in over the next few days."
Bendtner has scored 22 goals since he joined Arsenal in 2005, although he only managed two in the Premier League last season.