Badoer, the 38-year-old test driver making his comeback nearly a decade after his last race, struggled as a replacement for injured Brazilian Felipe Massa [ Images ] in Sunday's European Grand Prix [ Images ].
The Italian has said he has the job until Massa returns, which may not be this season, but team boss Stefano Domenicali sounded less sure of that after Badoer was the last car to cross the line in 17th place.
"For us the first priority is to understand when Felipe Massa will come back," he told reporters. "For sure it is an important race for Luca next weekend. We are expecting a big jump from him and then we will see.
"As I have said before, Ferrari cannot be satisfied with a car in last position. That is pretty clear, but we need to consider all the circumstances and everything that has happened," said Domenicali.
Badoer, who has now started 50 races without scoring a point, picked up a reprimand and fines totalling 5,400 euros ($7,732) in Friday practice and qualified last on Saturday.
In Sunday's race he used the Ferrari's KERS energy recovery system to get up to 14th at the start but was then in a collision with Renault [ Images ] rookie Romain Grosjean.
He also spun and was handed a drive-through penalty for illegally crossing the white line on the pit lane exit after his pitstop.
"I think if you look behind, for sure it was a difficult weekend for him," said Domenicali.
"In terms of race pace, if you look and you compare to the other young drivers, you can make your opinion. He did a great start and then he was touched from behind so he lost a place.
"Everyone was worried this morning about his health, worried that it was not possible for him to get to the finish and that he would have to go to the hospital," said the Ferrari chief. "But he was very good.
"It is just not being used to racing. I am expecting a big step next week."
Massa to fly to Miami [ Images ] on Friday for more checks
Ferrari's Felipe Massa will fly to the United States on Friday to see a motor racing trauma specialist as part of his recovery from the life-threatening head injuries suffered in Hungary last month.
The Formula One champions said on Sunday the Brazilian would visit neurosurgeon Steve Olvey, who was medical director of the former CART series.
He has also worked with Formula One's governing body, the International Automobile Federation (FIA) in designing safer helmets.
"I will take my CTs (brain scans) with me and probably undergo further exams at the hospital in Miami," Massa said in a statement.
The Brazilian was struck on the head by a spring that broke free from compatriot Rubens Barrichello's [ Images ] Brawn car during qualifying in Budapest.
He watched from his bed in Sao Paulo on Sunday as Barrichello won the European Grand Prix in Valencia, the 37-year-old former Ferrari driver's first win in nearly five years.
Massa said he had called Barrichello, who carried a message to his compatriot on his helmet, to congratulate him as well as talking to Ferrari boss Stefano Domenicali and president Luca di Montezemolo.
"I was with my fingers crossed all the time, expecting a victory that could keep the Brazilian domination in Valencia," said Massa, last year's winner in the city from pole position.
"Rubens did a fantastic job today. I was checking his lap times and I'm sure he could win even without (Lewis) Hamilton's McLaren [ Images ] problem," he added.