A spokesman said Laudrup, the former Barcelona and Real Madrid midfielder who took charge at the Balearic Islands club at the end of the 2009/10 season, had told the board he had decided to leave for the good of the team.
The 47-year-old had expressed frustration with recent transfer policy, which he felt left him short of forwards, and his decision followed the club's announcement on Monday that they had sacked his number two Erik Larsen for criticising the board's policies in the Danish media.
The club published a statement later on Tuesday saying an agreement in principle had been reached for the cancellation of Laudrup's contract and it was likely to be signed on Wednesday.
"One of the important things in football is the climate in which you work," Laudrup was quoted as saying in local media after he called a post-training news conference.
"It cannot be that I have to go home every day feeling frustrated and angry," he added. "You can lose or win but you have to enjoy yourself."
Regarded as one of the finest playmakers of his generation, Laudrup also had stints coaching Mallorca's La Liga rivals Getafe and Russian club Spartak Moscow.
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