Robert Veres was the surgeon who operated on the Ferrari driver on Saturday night, and he has revealed that Massa's eye was hurt in the qualifying accident but doesn't "know the extent of this damage".
It is believed that tests have shown no major structural damage to the eye, but that more detailed examinations or treatment are not possible while he is in coma with more pressing health risks.
Ferrari president Luca di Montezemolo visited the central Budapest AEK hospital on Monday, and La Gazzetta dello Sport in Italy reports that he and team boss Stefano Domenicali will return by private jet on Tuesday.
Montezemolo said: "The most important thing is the recovery of the man, not the driver. We have now returned to Maranello but tomorrow we will be back with Felipe."
He added that Ferrari's priority is Massa's health, but that the team will not "wait too long" before considerations about his replacement begin.
It is also reported, by Brazil's TV Globo, that Massa may be transferred later this week from Budapest to Paris' Pitie-Salpetriere hospital, which has links with the FIA and has treated patients including Michael Schumacher and Ronaldo.