Rovers were sent down when the decision was taken to settle league placings on a points-per-game formula last week.
The decision saw Sunderland finish outside the play-offs and facing up to the reality of another season in the third tier.
Tranmere felt particularly aggrieved given they had a game in hand and had won each of their last three matches.
Palios, in a statement, wrote: “Emotions are running very high, but our first duty is to act in the best interests of the club.
“We have been taking detailed legal advice from experts in this specialist field of litigation and are closely following the legal actions in Belgium, France and Scotland (amongst other places) where similar decisions are being challenged and overturned on the basis of anti-competitive behaviour and unfair prejudice.
“At this stage we are keeping an open mind as to what legal action may be appropriate and/or necessary, and the timing of that.
“Our preferred option is of course to resolve the dispute in an amicable fashion working together with the EFL – and we invite the EFL to do so with the best interests of the footballing pyramid in mind – but to date the EFL has given no indication of any inclination to work with us to find a reasonable solution without resorting to formal legal proceedings.
“Accordingly, all options remain open, including a legal challenge if required.”