Having sold Paul Robinson to Blackburn and Radek Cerny to QPR, Spurs are looking for a back-up to new Brazilian No.1 Heurelho Gomes.
Bywater is currently at Derby but slipped down the pecking order behind ex-United keeper Roy Carroll and spent the second half of last season on loan at Ipswich.
Derby boss Paul Jewell said: "Tottenham came in with a bid for Stephen and the player is very keen to go, which is fully understandable.
"I would like to have kept him but it is a move which appeals to him and we wish him well."
Bywater, 27, left Rochdale as a teenager for around £250,000 without playing a game to join West Ham. Tweet

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Correction: He played one game the week before his transfer was finalized. It was the Auto window shields cup game and Carlise won 6-0....so he was officially Rochdales worst ever keeper lol
But we knew for many years he was a very talented keeper with the England under 19 side etc.
My next door neighbours son was on the same goalkeeping course as Stephen when he attended Manchester City's Centre of Excellence they were both 9 years old.Stephen was the only one that was eventually kept on by City. I was told that Rochdale offered Stephens Dad the job of running Rochdales Junior set up with the proviso that he brought Stephen then 12 with him . I don't think that under the rules that apply now Rochdale could have done that without paying City a lot of compensation.