Rangers appeared to be on the verge of bringing Bryan to Ibrox, only for the deal to collapse at the medical stage, according to the Scottish Sun.
Rangers boss Steven Gerrard later told BT Sport, however, that the club had failed to reach an agreement with the Manchester City defender, who wanted to 'keep his options open' - and Sheffield United could be the ones who profit.
That said, the Sun's claim about the structure of the proposed deal suggests the Blades have reservations about signing the 21-year-old, which may or may not relate to those reports of an unsuccessful medical.
Some fans have speculated that United's Bryan interest could be linked to Brighton's pursuit of Jack O'Connell, although the Seagulls have now turned their attention away from the Bramall Lane star, according to the Argus.
Rangers, meanwhile, remain on the hunt for a left-side centre-half, after links to Millwall's Jake Cooper and Blackpool's Curtis Tilt of Millwall came to nothing.
Could Rangers regret their apparent failure to sign Bryan?
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