Edwards has been turning heads in the Championship this season despite being only 19 and several clubs have taken note of his performances in a struggling Posh outfit.
His composure at the back has impressed several Premier League scouts and he is being tipped to move on from Peterborough in the summer.
There is serious interest from clubs in the Premier League ahead of the next transfer window.
And it has been claimed that Spurs and Palace are two clubs who are closely tracking his performances in the Championship.
They have been happy with what they have seen from the 19-year-old defender and are considering getting their hands on him.
Tottenham are planning to sign Edwards with a view to loaning him out in order to aid his development.
The teenager, who has appeared 31 times in the Championship this season, has three years left on his contract with Peterborough.
