Ake has established himself as a regular starter for the Cherries since his move from Chelsea, with his performances during the opening stages of this season in particular drawing the attention of some of the Premier League's biggest clubs.
Manchester United have already been linked with the 23-year-old as a possible solution to their defensive issues, and Eurosport reports that Tottenham are now also considering an approach.
Spurs failed to make a single signing during the summer transfer window, but manager Mauricio Pochettino is eager to bolster his defensive options following an injury to Jan Vertonghen.
The 31-year-old has been ruled out until December, prompting Pochettino to begin thinking about a long-term replacement given that Toby Alderweireld's future is also up in the air.
Ake is thought to fit the mould for Pochettino, although any deal for the Dutch international is likely to cost around £40m - double what Bournemouth paid for him last year.