Crafar earlier rejected an offer from the receivers for six months' free rent in Rotorua, if he left the farm on April 9.
Allan's brother Frank told KordaMentha he would move, but only if he was paid the six months' free rent offered by the receivers as a lump sum. Allan's son Robert was also understood to be residing on the property.
KordaMentha said it required the properties for current and incoming staff "so that we can continue to operate them effectively".
Litigator Michael Arthur, of Chapman Tripp, said he expected the whole process could take two to three months and was likely to be heard in a High Court.
Crafar would be given an opportunity to respond to the papers, before an application was heard in court where he would be required to spell out why he should be entitled to remain on the land.
If Crafar chose to defend court action, a further court date would then be set.
Chinese dairy investor Natural Dairy has a conditional sale agreement in place to buy 16 farms previously owned by the Crafar family, which range in size from 128ha to 1750ha.
That agreement was subject to Overseas Investment Office approval and could be overtaken by a better offer.
Tenders for the farms close on June 23.
Asked whether receivers would accept an offer from Crafar, KordaMentha said it would look at all offers.
Crafar said last week he was considering "three very good options" in an attempt to trade his way out of debt.
He said he hoped to be able to present those offers in the coming weeks.