The German outfit have supposedly held talks with Rangers regarding a move that could be worth around £6m.
However, since the report, a number of outlets have moved to deny these claims, including a spokesperson for Red Bull Leipzig.
Twitter: A simple email to Press Spokesperson BENJAMIN IPPOLITI for RB Leipzig from me pretending to be a journalist confirm… https://t.co/4R1gxRvfOP (@Gregco5088)
Sky Sports have also declared that there have been no bids or interest for McKay from any clubs.
Twitter: TRANSFER NEWS
Sky sources understand Rangers have received no offers for Barrie McKay following reported interest f… https://t.co/x6Wabx7NdC (@ScotlandSky)
The Record claim that RB Leipzig spotted McKay during the recent friendly between the two sides, in which Mark Warburton’s team lost 4-0.
The winger does only have 18 months left on his current Rangers deal and Leipzig sporting director, Ralf Rangnick, was apparently impressed with what he saw.
The Bundesliga new boys have got previous buying Scottish players, with them splashing out £13m on McKay’s Scotland teammate Ollie Burke from Nottingham Forest last summer.
For now, at least, this looks like a non-starter.