Defoe has a thigh problem which has affected his pre-season preparations for Sunderland.
The English striker is set for scans, with Stockdale remaining positive about the 33-year-old becoming full fit for the Black Cats’ opening league game of the season against Manchester City away from home at the Etihad Stadium.
“It’s too early to say - but we don’t want to take any risks,” Stockdale told The Sun. “We will deal with it once he’s had a scan, then make an assessment.”
Defoe is one of the best players on the books of Sunderland at the moment and will be key for the Black Cats next season.
It is hugely important for David Moyes’s side that the former West Ham United striker is ready for the start of the 2016-17 campaign.
The former Tottenham Hotspur striker scored 15 goals and created 21 chances in 33 Premier League appearances for the Black Cats during the 2015-16 season.
Sunderland narrowly avoided relegated to the Championship last season and will remain in the Premier League for the 2016-17 campaign.