Defoe, who joined Sunderland from Toronto FC in January, scored four goals in 14 Premier League games last season. But, the 32-year-old is hoping to have a bigger impact during the 2015/16 season.
In addition to his aim of scoring 20 goals, Defoe is also looking to remain fit and healthy during the build-up to the new season.
"During the off-season I always keep myself fit," he told Sky Sports. "I try not to eat too much and get the rest – the season is so long – but after a couple of weeks I'm ready to go back, ready to train.
"Hopefully we'll have a good pre-season and we can start the season really strong. People say you should always aim for 20 goals in a season and if I'm scoring goals it's only good for the club and the team."
Defoe added that he was delighted that manager Dick Advocaat has signed a one-year extension, with the 67-year-old initially having indicated that he would be retiring at the end of last season. However, he performed a U-turn and opted to stay at the Stadium of Light for another season.
"He [Advocaat] just said from day one that all he wants is for the players to be sharp every day in training, apply yourselves and do the same in the game," Defoe said. "If you don't want to do that in training, then you won't play, it's as simple as that. He doesn't care who you are.
"When a new manager comes in, it keeps you on your toes and with someone like Dick, who has been in the game so many years, you respect someone like that."