The France international, 32, had surgery to remove a tumour from his liver last year, but after returning to play again, was forced to undergo a transplant on April 10 with part of an organ donated by his cousin.
"It's up to him. I wouldn't stop him. Time will tell," doctor Juan Carlos Garcia-Valdecasas was quoted as telling Spanish television station TV3 on Thursday. "If Eric responds well, there is no reason why he shouldn't.
"The liver is an organ that regenerates in three months. Abidal has to recover little by little, but between three and six months, or up to a year after the intervention, the patient is able to have a normal life.
"He is always in high spirits. He is a very positive character, it is tremendous. He has never complained about anything."
Barcelona players draped a shirt with his name on it over the trophy when they celebrated winning the Copa del Rey final against Athletic Bilbao last Friday.