The ex-Kilmarnock star is contracted to Bolton Wanderers, but the Lancashire side have entered administration and dropped into League One which could see the forward moved on.
According to the Belfast Telegraph, Rangers have had talks with the player's representatives, who cost the former Premier League side £400,000 from Charlton.
Magennis is familiar with Scottish football having played for St Mirren, Aberdeen and Killie.
The 28-year-old was a versatile and somewhat misunderstood player before arriving at Rugby Park where he transformed into a dangerous and powerful forward.
Having made his debut for the Northern Ireland national team back in 2010, it wasn't until 2014 when he became a regular - he now has 41 caps to his name.
If he signs for Rangers he will become the club's fourth Northern Ireland star, joining Kyle Lafferty, Jordan Jones and Steve Davies.