International chief Michael O'Neill currently has four players on the books at Ibrox - Steven Davis, Jordan Jones, Kyle Lafferty and Gareth McAuley - and the Belfast Telegraph understands the Light Blues are in talks with Magennis' representatives.
Magennis, who scored the winner for Northern Ireland against Estonia in Tallinn last Saturday night, is currently in limbo with his club Bolton Wanderers.
The Bangor lad has one year left on his contract after signing from Charlton Athletic last year for £400,000.
But with Bolton entering into administration following financial issues and the Lancashire club relegated from the Championship, Magennis may be sold or simply allowed to leave on a free transfer to help balance the books at the cash-strapped club.
Magennis has extensive knowledge of the Scottish Premiership having played for Aberdeen and Kilmarnock and would be a powerhouse striker for Steven Gerrard's men.
Lafferty and McAuley are expected to leave Ibrox this summer after failing to make an impact last season, but Magennis would relish the opportunity to be a star in the west end of Glasgow.