According to The Sun newspaper the 40-year-old actor and TV presenter was booked to join Take That star Gary Barlow, 50, to perform their festive single How Christmas is Supposed to Be on the pre-recorded episode of the BBC dance show, due to air on Christmas Day.
A spokesperson for Strictly Come Dancing declined to comment.
The BBC announced last week that the Strictly Christmas special would feature two very special performances from Jamie Cullum and Gary Barlow and Sheridan Smith.
The West End star - who appeared on The Jonathan Ross Show on ITV last week with Barlow - apparently pulled out just days ago, leaving the Take That singer to perform alone.
A representative for Smith also declined to comment.
The Strictly Christmas special is due to record at Elstree Studios in North London this week.
It will feature all-new guest celebrities on the dancefloor including singer Anne-Marie, newsreader Moira Stuart, First Dates star Fred Sirieix and The Repair Shop's Jay Blades.
Smith announced in July that she and fiance Jamie Horn had separated after three years together.
In October she revealed she had been upset by abusive messaged from online trolls after she shared an Instagram selfie with new boyfriend Alex Lawler.
Smith confirmed in September she was dating old flame Lawler, who appeared in Sky One football TV drama Dream Team between 2002 and 2005 and has since moved behind the camera.
In November she shared on social media that she was feeling the strain of trying to balance work with looking after 18-month-old son Billy.
Smith posted a meme that read: "I would like to work full-time and also be with my kids full-time. And I would like a unicorn that is also a time machine."
She added: "Please send help!"
Smith previously opened up about her mental health battles in ITV documentary Becoming Mum, giving producers exclusive access to her life in the four months leading up to the birth of her son.
This year she has presented BBC dog grooming show Pooch Perfect – which has not been renewed for a second series – and was a guest judge on RuPaul's Drag Race UK.
She is also one of the celebrity panellists on new ITV show Starstruck, along with Olly Murs and Adam Lambert, which will see members of the public transformed into their favourite pop stars to perform with the celebrities.
The Cilla star – who lost her father Colin to cancer in 2016 – has previously opened up on her struggles with anxiety, panic attacks and alcohol misuse.
She recently published her memoir Honestly.
Watch: Sheridan Smith attending a Christmas party in 2019