Slade presided over four successive wins before parting company with the club on Monday.
In a statement, Fry apologised to supporters for a lack of information surrounding the events but said it was unavoidable.
"I would like to be in a position to explain the reasons why it was necessary for Russell and the club to part company but I am currently unable to do so for legal reasons," he said.
"I'm positive that our fans would completely endorse the decision of the board if I was able to share full details of the circumstances.
"But for the moment I am, unfortunately, bound by confidentiality issues."
Yeovil remain eight points clear of relegation having played a game more than all bar one of the teams below them.
A host of candidates have been linked with the Huish Park hotseat, including Thompson, John Ward, Steve Cotterill, Leroy Rosenior and former player Alan Pardew.
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