"I'm glad to reach the semi-finals in this tournament, but to be honest now, as I say always, health is the first of all of my life", Del Potro said.
"Then I will take a decision for tomorrow".
Federer broke Gasquet at 5-5 to gain the advantage and went on to take the first set.
Federer cranked up the gears in the second set, breaking Dolgopolov twice to seal victory after exactly an hour on court.
Nadal, who extended his winning streak to 15 matches, pegged Dimitrov back with relentless baseline hitting to take the first set easily.
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Nadal also improved his win streak to 15 having won the China Open last week.
The second set was a close one as both players held all of their six serves and had to fight in the tie-break. In Beijing, he defeated Dimitrov in a three-set semi-final.
Here, Dimitrov extended their quarterfinal to a third set when he rebounded from a 4-2 deficit to win the second-set tiebreaker.
"Winning a lot of matches in a row, so I'm very happy for everything", Nadal said.
Fognini was playing the day after being handed a suspended ban from two grand slams and $96,000 (A$123,000) fine for verbally abusing a female umpire at the US Open.
Nadal, who has never won the title in Shanghai, will face fourth seed Marin Cilic in the last four.
The 2014 US Open champion knocked out Spain's unseeded hopeful Albert Ramos, 6-3, 6-4.
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