Currently at Blackburn Rovers - for whom he has scored 49 Championship goals over four seasons - the 34-year-old ex-England youth international is contracted until mid-2020.
However, Wanderers could sign the former Swansea City, Sunderland and Middlesbrough man as a free agent were he able to win a release, much in the same way as Adam Le Fondre did in securing a mutual termination from Bolton Wanderers to join Sydney FC last season.
Graham finished Rovers’ second top scorer in 2018-2019 with 15 goals but can no longer be guaranteed a starting spot by coach Tony Mowbray and might be tempted by an Australian adventure to round off a 15-year professional career.
He has made two league starts and four appearances off the bench for one goal since the start of the new campaign, with Rovers sitting 17th with seven points.
Wanderers are looking to add venom in the final third as none of their existing attacking options, the likes of Mitchell Duke, Kwame Yeboah or Bruce Kamau, possess a compelling strike rate.
Graham has amassed 150 career goals, with further stints across the divisions at Carlisle, Watford, Blackpool, Derby, Hull and Wolves.
The World Game contacted Western Sydney Wanderers for comment.
