The 22-year-old made the switch from Villa Park to Bramall Lane ahead of the 2023-24 season, in a deal worth £18m for the Englishman.
Archer enjoyed a productive loan spell at Michael Carrick's Middlesbrough last term, netting 11 Championship goals in 22 appearances as the Teesside club reached the playoffs.
Featuring in 22 Premier League matches for the Blades so far this campaign, the England Under-21 international has bagged four top-flight goals for the strugglers.
According to Birmingham Mail, Aston Villa and Sheffield United have a deal in place which would see the former re-sign Archer if the Blades do not avoid the drop.
The report claims that the Villans and Chris Wilder's men have already shaken hands on a transfer fee, which is understood to be significantly less than the £18m that United spent in the summer.
Despite a much-needed 3-1 success over relegation rivals Luton Town on Saturday afternoon, the Blades remain rooted to the bottom of the Premier League standings, seven points from safety.
Archer started his first top-flight match this weekend since the reverse fixture against Rob Edwards's Hatters at Bramall Lane on Boxing Day, opening the scoring in the 30th minute.
After playing a key part under former boss Paul Heckingbottom, the arrival of new manager Wilder and January signing Ben Brereton Diaz has led to the 22-year-old falling down the pecking order in Yorkshire.
Scans on the Chilean earlier this week revealed a hamstring injury, with the former Blackburn Rovers man missing the victory at Luton as a result.
As well as Blades poacher Archer, Unai
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