Sports daily Mundo Deportivo said on Sunday that Puyol had told "various team mates" that he might end his career two years before his contract expires in 2016 if he continued to have problems with his right knee.
The 35-year-old Spain central defender, who has been at Barca since he joined their academy nearly 20 years ago and is hugely popular with the fans, has also been sidelined over the past 18 months by a fractured cheekbone and a dislocated elbow.
"The only thing I have to say is that he has not spoken to me about this issue," Martino told a news conference ahead of Tuesday's King's Cup last 32 second leg at home to third-tier Cartagena.
"He is training normally and pushing himself to the limit," added the Argentine. "I know that he has never said that (he planned to retire) and therefore it is not necessary that he comes out and denies it."
Barca won the first leg at Cartagena 4-1 and Martino said the return would be a good chance for his players to build on the fine form they showed against Celtic in the Champions League last week and in Saturday's La Liga match against Villarreal.