The Spain international had struggled with the injury for much of this season, before undergoing surgery in his native Brazil in December.
The club are confident the operation was a success and believe he will be back in action by mid-February.
A club statement said:
‘Diego Costa has entered the second phase of his recovery after returning from Brazil, where he underwent an operation on his left foot on December 5,’ a statement said.
‘Our striker is making progress in his rehabilitation and sport readaptation process. Apart from the daily physiotherapy and aerobic training on a stationary bicycle, a specific swimming pool routine is to be added shortly.’
Juventus president Enrique Cerezo hailed the striker’s role for the club as he provided further information on his timescale for recovery.
He said: ‘The only thought is to recover Diego Costa for the double challenge against Juventus. Diego is very important for us and in these matches he thrives.’
The Spanish club host Juve in the first leg of the second round tie on February 20, while the return is scheduled for March 12 in Turin.