A 24-16 win over Munster on Sunday saw the French side book their place in the final of next month's Heineken Cup against Saracens.
Toulon also currently sit at the top of their domestic league, where they have secured a spot in the end-of-season playoffs.
Despite his team's success this year, Laporte is quick to dismiss their chances of doing an impressive double.
"Mathematically, yes, we can talk about it. But it's simply unthinkable to dream about it for one second when you know a bit about high level sport," he is quoted as saying by BBC Sport.
"Talking about the double seems stupid. Sport at such a level is never predictable. Saracens are a machine. They are far ahead in the English championship and they are an ambitious club."
Toulon will meet Saracens in Cardiff for the Heineken Cup final on May 24.