Laporte's men are also fighting for glory in the Top14 and currently sit in third place in the French standings with just one game of the regular season remaining.
Only the Toulouse team of 1996 have won European and French trophies in the same season but Laporte knows the only way his side have a chance of matching that achievement is if they truly believe in their capabilities.
"We must believe we can win both trophies. I believe in it," said Laporte, whose face Lyon this Saturday before travelling to London next week.
"Still playing in both competitions now only adds one game to the calendar.
"We haven't won anything yet and we are not the best in the Top14. Toulouse and Clermont are in the top tier and we are with Castres, Racing Métro and Montpellier in the second tier. But if we are not better than anyone we are not worse than anyone either. That is the message I have been telling my players: 'Yes, we can do it'.
"The goal this season in the Top 14 was to be in the top six. So we could be satisfied that achievement now, but I want more. I have told the players that I want us to be ambitious. I want to win everything. I want to win every single game.
"I know we have some weaknesses but I do not want to even think about defeat. We trained hard during the winter just to be ready for this stage of the season. My message is clear: We are not afraid of anyone."