Kane picked up the World Cup Golden Boot award as England made it all the way to the semi-finals in Russia this summer, but his performances towards the latter stages of the tournament led to questions whether he was carrying an injury or suffering from fatigue.
The 25-year-old's displays for Tottenham Hotspur so far this season have also led to suggestions that he may need a rest, despite breaking his August duck in the Premier League.
The Mirror reports that Southgate will hold talks with the Spurs striker regarding his fitness ahead of Saturday's UEFA Nations League clash with Spain at Wembley.
Tottenham are confident that Kane remains fully fit and the England captain is expected to start against Spain, although he could be rested for the friendly against Switzerland three days later.
Kane has featured in all four of Tottenham's Premier League games so far this season, despite only returning to training with the club five days before the start of the new campaign due to his involvement in the latter stages of the World Cup.