The 27-year-old has been a regular figure for the Blades since their return to the Premier League in August, scoring once and assisting once in six league appearances.
Paul Heckingbottom's men have struggled since their promotion from the Championship in May and are yet to pick up their first win of the term, meaning they sit bottom of the top-flight standings.
McBurnie secured a switch to Yorkshire from Swansea City in August 2019 and has since made 143 appearances for the Blades, finding the net on 24 occasions over a four-year period.
According to the Daily Record, Rangers are considering a move for McBurnie in next year's summer transfer window, with the striker's time at Bramall Lane potentially coming to an end.
The former Barnsley man is a key part of Heckingbottom's side in the top flight despite the arrival of Cameron Archer from Aston Villa before the start of the season.
Despite this, McBurnie's contract with United expires at the conclusion of the 2023-24 campaign, leading to speculation that he could be set to move on.
As the 16-time Scotland international approaches free-agent status, he would be able to hold discussions with potential suitors from January onwards ahead of a possible summer switch.
One of the reported destinations for McBurnie is his boyhood club Rangers, with the Scottish giants looking to rebuild their squad and fortunes under new stewardship in the dugout.
The Glasgow-based club are currently second in the Scottish Premiership standings but trailed title rivals Celtic by seven points ahead of this weekend's round of fixtures.
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