Vaughan told BBC Sport: "I'd be making a few phone calls to legal sources to try to take this a little bit further. I can't think of anything worse than your name mentioned in terms of fixing a game of cricket."
Butt's claims, for which he later admitted he had no proof, sparked outrage.
Strauss expressed disappointment that England's "integrity" had been questioned, and revealed "strong misgivings" about continuing the one-day series against Pakistan.
Vaughan, captain between 2003 and 2008, said: "I think Andrew Strauss and the team have dealt with it in a very good fashion. They've kept their dignity and they've not said much.
"I've never been involved with England team through that kind of allegation or finger-pointing.
"But I'd be taking it as far as I can because unless Ijaz Butt takes back the comments, I think this case will go on for a lot longer."
Vaughan calls for full investigation
Butt's ill-fated intervention came after the International Cricket Council announced an investigation into Pakistan's performance in the Oval contest after receiving reports about "scoring patterns" during their innings.
Pakistan set England 242 to win the game but the hosts lost their last five wickets for 17 runs.
On Sunday, Butt told India's NDTV channel: "There is loud and clear talk in bookie circles that some English players were paid enormous amounts of money to lose. No wonder there was total collapse of the English side."
However, speaking to BBC Radio 5 live, Butt later claimed he was only stating what he had heard and that he had no proof that England's players had thrown the game at The Oval.
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