Evans, 27, retired against Germany's Dustin Brown in the recent Surbiton Trophy with a calf injury, missing this week's Nottingham Open as a result.
Argentina's Del Potro, 28, is still struggling with the groin problem that hampered him at the French Open.
It is not known if they will be fit for Wimbledon, which starts on 3 July.
French Open winner Rafa Nadal pulled out of the tournament last week after being advised to rest by his doctor.