Alongside regional leaders, US Secretary of State Antony Blinken will attend the meetings
The top seed has been in overwhelming form in New York and has yet to drop a set or even his serve in four outings.
Against compatriot Verdasco, Nadal enjoys a 10-0 win-loss record and their last meeting in the Monte Carlo Masters final in April ended in a 6-0, 6-1 rout in favour of the world number one.
Nadal though says he is taking nothing for granted against Verdasco who battled through four hours 23 minutes to reach the last eight against another Spaniard, David Ferrer.
‘He’s a very complete player. He has all the shots and he’s playing very well, no?’ Much better than he did in the last months, so it’s going to be a very difficult match,’ he said.
‘I saw him play today (against Ferrer), and I saw him play against (David) Nalbandian the other day.
‘He’s playing very good tennis, so it will be a very interesting match. I have to play aggressive, to play well.
Nadal has much to play for as he is bidding to become the youngest player to complete the set of all four Grand Slam titles having previously won five French Opens, two Wimbledons and one Australian Open.
Rather than dwelling on the last match between the two men, Verdasco will look to the classic semi-final they played in the 2009 Australian Open when Nadal won 6-4 in the fifth set.
He came back out two days later and incredibly defeated Roger Federer, also in five sets, to win his first title Down Under.
‘Everybody knows that he’s No. 1 in the world; he’s a great player,’ Verdasco said.
‘My record is not good against him. But I will keep trying and keep fighting to make the first time here.’
The other semi-final in the top half of the draw is a more unexpected affair with Switzerland’s Stanislas Wawrinka, playing in his first Grand Slam quarter-final, taking on Mikhail Youzhny of Russia.
Wawrinka, seeded 27, has shown a new side to his character and game in New York having taken on as coach Peter Lundgren, who worked with Roger Federer from 2000 to 2003 and then Marat Safin.
He used an aggressive, physical approach to down fourth seed Andy Murray in the third round and then played a cagey, tactical game to take out the final remaining home hope, Sam Querrey.
Youzhny and Wawrinka know each other well, and stand 2-2 in their head-to-heads, the Russian winning their only encounter this year in three sets at the Miami Masters.
‘He’s a tough player,’ Wawrinka commented.
‘He’s really strong player from the baseline. He has a great backhand. We already played sometimes together. I think we always have a tough match.’
Alongside regional leaders, US Secretary of State Antony Blinken will attend the meetings
Twice Grand Slam champion Alcaraz is set to make his Olympic debut while Nadal will be eyeing his third gold medal after wins in Beijing and Rio
The quake was at a depth of 503.2 km
The defending champions overpowered TP Mazembe from the Democratic Republic of Congo 3-0 in Cairo
Although the Gunners are top as they chase a first title for 20 years, Manchester City are regarded as statistical favourites to win a fourth successive crown
Doctors urge residents to take such situations seriously: 'Sharp objects can pierce the food pipe and can migrate into areas like the chest, causing further complications,' an expert says
Highly-rated 19-year-old Turkish midfielder Arda Guler scores match-winner on his first La Liga start
The special incentive allows eligible companies to obtain interest-free loans of a maximum of Dh300,000 with a grace period of 6 to 12 months