The newspaper claims Liverpool are looking into making a loan signing after Dejan Lovren joined fellow centre-backs Joe Gomez and Joel Matip on the sidelines this week.
But it adds that finding a top-quality available on short-term deal 'looks a big ask', with Burnley looking for around 14 times the £3.5 million they are said to have paid for Tarkowski back in 2016.
Crossed wires in the Sun's editorial department?
Although the Sun's headline states that Liverpool have made a 'shock loan move' for the England international, there is nothing within the article which substantiates that claim.
And it is perhaps more accurate to say Tarkowski is simply of interest to Jurgen Klopp's side at this moment in time.
The 26-year-old was able to capitalise on Michael Keane's sale to Liverpool's rivals, Everton, 18 months ago, going on to earn his first caps for England early last year.
Would the Burnley defender be a good addition for Liverpool?