Borriello suffered the setback in the first half of Roma's 1-1 draw with Sassuolo on Sunday and was expected to be out for a prolonged spell.
But tests on Wednesday confirmed that there was no damage to his ankle and coach Rudi Garcia, who is already without captain Francesco Totti, will not be deprived of the 31-year-old's services.
"Marco Borriello underwent medical tests this morning that revealed no damage to his ankle's ligaments or capsule," a statement on the club's official website said.
"The forward then underwent a session of physiotherapy."
There was also good news on the fitness of Totti, who has been out since mid-October with a hamstring injury but is now making good progress.
However, Adem Ljajic was not involved in training due to a muscle strain.
"Totti underwent physiotherapy before working out in the gym and running on the field," the statement added.
"There was separate training on the field and physiotherapy for Ljajic, due to a strain to his left thigh."
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