The 23-year-old Spaniard, whose elder brother Aleix also rides in MotoGP, broke the second metatarsal in his left foot during qualifying for last weekend's Malaysian MotoGP.
Espargaro was still able to take part in the subsequent race in Sepang, finishing a creditable sixth.
And with no further damage done to his injured foot, the Yamaha Tech3 rider - currently sixth in the championship standings - is on course to compete in Valencia next weekend.
Surgeon Dr Xavier Mir is quoted as telling the MotoGP website: "I already saw Pol in Malaysia and saw there that he had a fracture in the second metatarsal, with some displacement. Sideways movement was bearable but not forward to backwards movement.
"In Barcelona [Espargaro's home city] we repeated the radiography after an epic race in which he finished sixth. I can't understand how he endured the pain.
"But we've seen that the fracture hasn't moved. It's still in the correct position and this does rule out the requirement for surgery."
Espargaro will undergo a further X-ray next Wednesday to determine whether his injury has worsened.
Dr Mir added: "He will probably be uncomfortable with the injury at Valencia, especially as it's his left foot which is used to change gears.
"But considering how well he did at Malaysia he should be fine at Valencia. We will continue to monitor the injury to ensure that no displacement occurs and at the Grand Prix we'll evaluate whether he needs a painkilling injection.
"Ideally he wouldn't need it but we'll see how he is in practice."