New Zealand international Reid is out of contract at the end of this season, meaning he is free to join any club of his choice in July.
Arsenal and Liverpool have both been strongly linked with moves to sign the 26-year-old, who won West Ham's player of the year award back in 2013.
The former Midtjylland defender has developed into one of the top defenders in the Premier League in recent years, and interest in his signature is no surprise.
Yet now, the Mirror believe that it's Tottenham who will land him this summer, and not Arsenal or Liverpool in a deal which will frustrate West Ham.
The Hammers have been trying to extend Reid's contract beyond the end of the season in order to avoid losing him for nothing, but their efforts appear to have fallen short.
The Mirror report that whilst Reid can't sign a pre-contract agreement with another Premier League club under current regulations, West Ham believe that he has a gentleman's agreement to join Spurs in the summer on a free transfer.
With Younes Kaboul and Vlad Chiriches both linked with exits from White Hart Lane, it's no surprise to see Spurs considering a move to sign another centre back - and weakening one of their London rivals just makes the deal even more appealing.