Meekings went unpunished for blocking a first-half goalbound header from Leigh Griffiths with his arm on the goalline but will be sanctioned in retrospect.
Inverness won 3-2 in extra-time to secure a final next month with Falkirk but Meekings could miss out, despite Inverness rejecting the offer of a one-match ban from the Scottish FA for "denying the opposing team an obvious goal scoring opportunity by deliberately handling the ball".
Celtic had asked the SFA why Meekings' handball was not spotted.
"The club intends to vigorously defend our player and is taking legal advice on the issue," Inverness said in a club statement on Tuesday.
"Inverness Caledonian Thistle FC can confirm that it has declined the fixed one match suspension offer in relation to the notice of complaint issued to Josh Meekings following an alleged breach of Disciplinary Rule 200 at the ICTFC v Celtic game on Sunday, 19th March 2015."
(Reporting by Justin Palmer, editing by Pritha Sarkar)
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