On Tuesday the FIA announced its Compliance Department was looking into allegations made in a dubious publication suggesting Mercedes team boss Wolff and his wife Susie, who heads FOM's F1 Academy, were exchanging confidential information.
The probe took all parties involved by surprise and invoked a furious response by the Wolffs, Mercedes and F1's management. F1 and Mercedes rejected the allegations and condemned the lack of communication from the governing body over its pending investigation.
Amid speculation that rival teams had complained to the FIA about the Wolffs, all nine remaining F1 teams disputed they were behind the probe with statements backing the pair on Wednesday.
On Thursday the FIA then backtracked and announced that there would be no formal investigation after being satisfied that there was no "unauthorised disclosure of confidential information".
In a statement released by Mercedes on Friday, Toto Wolff said his team was in an "active legal exchange" with the governing body after seeing his and his wife's reputation damaged by this week's events.
Given the possible legal consequences of the row, Wolff said there would be no further official comment for the time being.
"We understand that there is significant media interest in the events of this week," Wolff's statement read.
"We are currently in active legal exchange with the FIA.
"We await full transparency about what took place and why, and have expressly reserved all legal rights.
"Therefore we ask for your understanding that we will not be commenting officially for now, but we will certainly address the matter in due course."
Susie Wolff also made further comments on the matter on Friday, slamming the FIA for its lack of transparency.
"For two days, insinuations have been made about my integrity in public and through background briefings, but nobody from the FIA has spoken to me directly," she said.
"I might have been collateral damage in an unsuccessful attack on somebody else, or the target of a failed attempt to discredit me personally, but I have worked too hard to have my reputation called into question by an unfounded press release.
She added: "This episode has so far taken place without transparency or accountability."
