Rangers could pip Sunderland to highly-rated striker while Chris Martin's future set to be resolved
McBurnie has been linked with a move to Sunderland this month as Chris Coleman looks to bring a striker in before the transfer deadline.
The 6ft 2in frontman has yet to open his account with the Swans, but has appeared regularly in the Premier League this season.
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Hide AdThe 21-year-old hails from Leeds, but is a Scotland Under-21 international and boyhood Rangers fan, and the Glasgow giants have made a move to add them to their squad on deadline day.
Coleman has been linked with a number of strikers since pulling out of a deal to sign Derby County's Chris Martin after the player stalled over the move.
Martin is now on the verge of joining Championship rivals Reading, with reports saying he is having a medical at the Royals today.