The Dane is widely expected to depart before Saturday’s game with Stoke City.
Rovers are winless in eight league games and have dropped to 18th in the second tier.
The Lancashire club lost 2-1 at home to fellow strugglers QPR at the weekend and are now just five points above the third-from-bottom R’s, albeit with a game in hand.
Rovers have triumphed just once in their past 11 league matches and taken just five points from the last 33.
Tomasson has reportedly told players that his time at Ewood Park is coming to an end, with the future of club secretary Ian Silvester is also said to be in doubt.
Rovers saw a beat-the-deadline seven-figure move for USA striker Duncan McGuire collapse due to an administrative error.
The frontman was also wanted by Sheffield Wednesday, with the Red Rose outfit having appeared to win the race for his services after agreeing a fee with Orlando City.
It is thought that Rovers officials did not press ‘send’ on the Football League’s transfer system.
The mistake is the second administrative error for a January deadline day addition in the last 12 months after former Huddersfield Town midfielder Lewis O’Brien’s failed loan move to the club from Nottingham Forest in 2023.