Vilanova is battling parotid gland cancer, which has culminated in surgery, chemotherapy and radiotherapy, while the France defender was diagnosed with a tumor in his liver.
And Villa says his own battle to come back from a broken leg has been put into perspective by the pair's respective struggles with illness.
"When you compare my injury to the diseases Tito and Abidal have had, their problems have been a lesson in life; two incredible people. These examples give us strength. They are the ones who encouraged us, urging us to be strong and fight. You see that the little annoyances of life are futile," Villa told El Pais.
The 31-year-old, who missed many months of action after suffering a broken leg in December 2011, reveals he struggled to adapt to not being with his team-mates and playing football week in week out.
"Mentally, I was not ready because I had never lived with such an injury before. The doctors told me that I could not do anything in the first month, but I wanted to work," Villa explained.
"My friends told me: 'Enjoy your family,' but I did not stay at home and went to the gym instead. I talked a lot with Xavi, who has suffered from long-term injury, and he told me: 'David, the feelings come back.' "