Former Denmark international Laudrup quit after clashing with the board over transfer policy.
The cash-strapped Balearic Islands club are in administration and the appointment of Caparros, whom local media said was asking for 1.3 million euros to take over until the end of this season, would need the approval of the officials overseeing the process.
"We have an agreement in principle with Joaquin Caparros for him to be the Real Mallorca coach," Serra Ferrer, who is also the majority shareholder, said after a board meeting.
"We hope to sort out the last details tomorrow," he added.
As well as to discuss the appointment of a new manager, Monday's board meeting was called to try to resolve a dispute between Serra Ferrer and director general Pedro Terrasa over the direction of the club.
Assistant coach Miguel Angel Nadal, an uncle of tennis world number two and club shareholder Rafa Nadal, took charge of the team for Saturday's 2-2 draw at Osasuna and Serra Ferrer said he would remain part of the technical staff.
Mallorca have been seeking an injection of cash and president Jaume Cladera said on Monday the club had been talking to a potential investor. He gave no further details.
