Livi were granted a judicial review after raising a petition at the Court of Session in Edinburgh yesterday.
The club is looking at "certain actions taken recently by the Scottish FA in connection with the registration".
The Lions are refusing to comment further about what actions by the SFA have led to them going to the courts.
But it appears that they would not have received a fair and independent inquiry and it is being claimed that an SFA official furnished Dundee with information ahead of their own appeal against the fine, launched on the grounds that the punishment was too lenient.
Dundee, presently rightly relegated, want Livingston to be docked points instead of receiving a fine, an action that would sent the Lions to the first divison.
But the Dens Park outfit had been told that their appeal would only be heard after Livingston's appeal against the fine imposed for not correctly registering former Moroccan international Kachloul.
A Dumbdee spokesman said: "We have been taken completely by surprise by Livingston's decision to withdraw their appeal.
"Dundee have therefore referred the matter to their lawyers and are now awaiting their advice before making any further comment or decisions. "
Kachloul had joined Livi on an amateur basis outside of the transfer window, but Dundee produced evidence proving that he had been paid.
Livingston have argued that they had consulted the SPL and SFA before registering Kachloul.
There have been fears that, if the row ended up in the courts, it could delay the start of the new football season.
Nobody at the SFA was able to comment.