The 25-year-old Holland international missed the final five games of the last campaign after dislocating his shoulder during the 3-0 derby defeat by Sunderland on April 14.
Krul underwent an operation a few days later and then started the long process of working his way back to full fitness.
However, he has revealed via his Twitter account that he has been able to step up his rehabilitation.
Krul tweeted: "Just finished my first proper gym session of the new season. Shoulder is coming on well. Can't wait for season to start."
He made 31 appearances last season, despite missing seven games with a nasty ankle injury picked up in the 1-0 Europa League victory over Metalist Kharkiv in Ukraine on February 21, before his campaign came to a premature conclusion.
Harper and Rob Elliot deputised when Krul was unavailable or rested, but the 38-year-old will formally leave the club after 20 years on July 1 when his contract expires, leaving Elliot and youngster Jak Alnwick to provide the back-up.
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