Tomasson's relationship with the Blackburn board has been uneasy since he came close to leaving in the summer.
The Dane is believed to be unhappy with the Championship side's January transfer dealings, which included selling star player Adam Wharton to Crystal Palace for £22million and failing to agree a loan back in the deal.
When contacted for comment, Blackburn insisted Tomasson has not been sacked and remains under contract.
Tomasson led Blackburn to the brink of the play-offs last season but they are languishing in 18th place after a winless run of eight matches.
The 47-year-old has been in the job for 20 months, arriving Swedish side Malmo.
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At Malmo Tomasson won the Allsvenskan league title twice in 2020 and 2021 and was projected for a bright future.
A legendary striker as a player, the Copenhagen-born star won the Champions League with AC Milan and UEFA Cup with Feyenoord.
Retiring from playing in 2011, he went straight into coaching in the Netherlands wit Excelsior, Roda JC and Vitesse before impressing at Malmo.
Should Tomasson step down now, he'll miss a glamour fifth round FA Cup tie against former club Newcastle.
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Discussing the tie with talkSPORT after beating Wrexham in the fourth round, he said: "I was only at Newcastle for one year but I still follow the results.
"It's a great club, a big club as well, so I'm looking forward to seeing my old club at Ewood Park, not St. James Park."