The 22-year-old made the switch from Villa Park to Bramall Lane during the summer transfer window, with the fee reported to be in the region of £18m.
Despite suffering from a number of injury problems throughout the campaign, Archer has still managed 22 Premier League appearances for the Blades, scoring on four occasions.
Since making his debut for boyhood club Villa as a 17-year-old in 2019, the England Under-21 international has made 15 first-team appearances for the Second City club.
According to The Sheffield Star, Archer will definitely be returning to Aston Villa at the conclusion of the season should Sheffield United be relegated to the Championship.
The report claims that the Villans and the Blades have an agreement in place whereby Unai Emery's men are obligated to re-sign the attacker if the Yorkshire club finish inside the bottom three.
Despite replacing Paul Heckingbottom for club legend Chris Wilder, Sheffield United have been unable to turn around their fortunes in the Premier League this season.
The Blades currently occupy 20th position in the top-flight standings, 10 points adrift of Nuno Espirito Santo's Nottingham Forest in the relative safety of 17th..
It had previously been reported that Villa had an option to buy back Archer in the event of United's relegation, however it is now understood that the agreement is stronger.
Should the Bramall Lane club pull of one of the most miraculous escapes in Premier League history, Emery's side would still have the right to re-sign the 22-year-old 'at a pre-agreed price that is higher than the obligated one'.
Archer found the back of the net in Sheffield United's most-recent win, with Wilder's side beating fellow strugglers Luton Town 3-1 at Kenilworth Road on February 10.
Since then, the former Preston North End and Middlesbrough loanee has been sidelined with a calf injury, meaning that he has been absent for the Blades' last four fixtures.
Providing an injury update following United's 2-2 draw at Bournemouth on the weekend, Wilder stated that he is hopeful that Archer will be available for selection after the international break.
With the former Villa marksman taking up a space in the medical room, Oli McBurnie and January arrival Ben Brereton Diaz have formed a two-man strike partnership in recent games.