The striker is one of several Barca players to have been given an extended break due to their commitments with the national team over the summer.
However, the 32-year-old is now back at the club and beginning work ahead of the new campaign.
Suarez will return to full training with the rest of the squad on July 31.
The club are currently still in Japan and play their final game of the tour on Saturday against Vissel Kobe.
Barcelona will then head home for a Joan Gamper Trophy match against Arsenal on Sunday August 4.