Nadal, who has never won a Masters title in Paris, has to outperform the world number two Novak Djokovic at the tournament to stay at the top of the ATP tree.
And the 32-year-old will go into the clash with Verdasco in good heart. He has won 16 of their 19 encounters.
On Tuesday night, Djokovic ramped up the pressure on Nadal by advancing to the third round with a 7-5 6-1 win over Joao Sousa.
The 31-year-old Serb struggled in the first set to subdue the Portuguese qualifier. But he turned on the style in the second set to race into a 5-1 lead.
Just before serving for the match, Djokovic interrupted play to help a spectator who was taken ill. Djokovic fetched a towel for the man who was led away for further treatment.
The pause appeared to disrupt his flow. He had to save two break points before concluding the contest.
“In the important moments, I managed to get the right shots in play,” said Djokovic after his win. “I’m not 100 per cent pleased with my game. I missed a lot of shots from the back of the court. But at the end of the day, it's the first match, so it takes a bit of time to adjust."
Damir Dzumhur will be the four time champion’s next opponent after he upset the 14th seeded Greek Stefanos Tsitsipas 6-3 6-3.