The on-loan Liverpool defender set up Michael Ngoo's goal in the 1-1 draw at Easter Road before Hearts won on penalties to secure a League Cup final place.
Wilson played in the 2010 final for Rangers and was sent off for denying a goalscoring opportunity in a 1-0 victory over Rangers, sparking a one-match ban in the competition.
Wilson signed for Liverpool before Rangers began the defence of their trophy and left without serving the suspension.
Inverness were told on Monday that Wilson was eligible, and Hearts had checked this with the authorities before the game, but they are not yet satisfied by the explanations.
In a statement on Monday night, the club said: "As a result of discussions that have taken place throughout the afternoon, the club will be seeking further details and an explanation on events surrounding this matter."
The club had earlier said: "We have spoken to the SFA disciplinary committee who have confirmed that Danny was eligible to play on Saturday.
"This was checked out by Hearts and the SPL prior to Saturday's game.
"There was no notice of suspension accompanying his registration paperwork when he returned from Liverpool FC."
It is not clear when Wilson served any suspension for his dismissal, with the offence not serious enough to spark an automatic ban for Rangers` next league game.
Wilson made his Liverpool debut in the Anfield team's opening League Cup game of the 2010-11 season, a penalty shootout defeat in September against a Northampton team containing Inverness striker Billy McKay.
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