The 37-year-old secured a switch to the Belgian Pro League in the summer and has featured 13 time so far, keeping a clean sheet on two occasions.
Schmeichel continues to be an important part of his national side, having earned 99 caps for Denmark since making his debut in December 2009.
The Dane has legend status in the East Midlands after winning the Premier League under Claudio Ranieri at Leicester City, and he played 479 times for the Foxes between 2011 and 2022.
According to The Sun, Sheffield United are ready to enter the market for a goalkeeper during the upcoming January transfer window.
The report claims that the Blades are looking to provide competition for current first-choice stopper Wes Foderingham, who has made some high-profile errors in recent months.
It is understood that Chris Wilder's men would be keen on a loan move for a keeper in the New Year, although a permanent move has not been ruled out.
Sheffield United owner Prince Abdullah made business decisions over footballing decisions in the summer as he decided to sell Iliman Ndiaye and Sander Berge.
Schmeichel only joined Anderlecht in September but has recently discussed his openness to returning the Premier League - a competition that he was a stalwart in for many years.
There is understood to be some tension in the Belgian side's dressing room after the Dane immediately replaced Maxime Dupe in between the sticks once the ex-Foxes man had arrived.
The 30-year-old former Toulouse keeper has not featured for Anderlecht since the 2-2 draw at Kortrijk on September 17, sitting on the bench for the last 12 Pro League fixtures.
Although Foderingham cannot take the blame for all of the Blades' struggles, Wilder's side possess the poorest defensive record in the Premier League this season, conceding 49 goals in just 20 contests.
Following a four-game run without a victory, Sheffield United will cherish the welcome distraction of the FA Cup when they travel to League Two Gillingham on Saturday.