Bitter Dundee had asked for an investigation into possible payments to the Moroccan.
Livi chief executive Vivien "no nonsense" Kyles said: "Livingston FC are greatly disturbed by the ridiculous accusations about the signing.
"When Kachloul signed his contract, he was registered with full consultation with the SPL."
There are claims that the former Aston Villa and Southampton player was paid £4,000 per week to double up as a business development manager.
Dunfermline voiced concern to the Scottish Premier League seven weeks ago and, this week, relegated Dundee have followed that up with a letter.
Kyles hopes that the SPL will resolve the dispute.
"They were very helpful at that time and I would urge them to settle the matter as soon as possible," she said.
Kachloul has insisted he did nothing underhand while helping Livingston avoid relegation.
"This can easily be clarified by the people at Livi," he said.
"I have done nothing wrong and Livi deserve their place in the Scottish Premier League. The team proved it on the pitch."
Kachloul could not receive payments from the \Lions for playing and had to sign as an amateur because he joined Livingston outwith the transfer windows.
He would not go into detail about whether he received payments other than the permitted legitimate expenses.
But he added: "It's quite sad for clubs to go this way. They are blowing smoke around the real story."
Fanzine View -
What a disgrace, Dunfermline are a joke of a side that is run by a man that must me the most hated man in the SPL, and Dundee, a joke of a team that has a disgrace of a support, a first division side that'll not be missed in the SPL.
Below is the statement on the official Livingston FC site, www.livingstonfc.co.uk and copyright Livingston FC.