The newspaper claims Tottenham tried to sign Green two years ago, only for the winger to extend his Villa deal by a further three years instead.
Tottenham are short on natural wingers after allowing Georges-Kevin N'Koudou to join Burnley on loan earlier this week.
And Aston Villa's financial situation - Bruce's January spending is thought to be severely restricted by FFP - may offer the Londoners and Bournemouth hope of prising Green from Villa Park.
The 19-year-old made his Villa debut in March 2016 and has gone onto play a further 25 times for his local side, scoring once.
Could Green be prised away from Aston Villa this month amid alleged interest from Tottenham Hotspur and Bournemouth?