Davies has been at the centre of an apparent transfer tug-of-war between Spurs and Liverpool, with both clubs seeing the 21-year-old as a long-term solution to their problems at left-back.
The Wales defender was expected to choose Champions League football at Anfield and a reunion with former Swansea boss Brendan Rodgers but Tottenham have moved quickly since having a bid accepted earlier this week.
Both Swansea and Spurs are currently on a pre-season tour in America, which has been to Tottenham's advantage in conducting negotiations.
Davies played 45 minutes in a 1-1 draw with Chivas Guadalajara on Wednesday and was due to play in Swansea's final tour fixture against Minnesota United on Saturday before the squad flies home.
Garry Monk wants to use any deal with Tottenham to engineer a return for midfielder Gylfi Sigurdsson, who scored seven goals in 18 league appearances during a five-month loan spell at the Liberty Stadium in 2012.
The club are unlikely to pursue Sigurdsson as a stand-alone transfer, however, should Davies' move to White Hart Lane fall through.
When contacted on Saturday, Swansea were unavailable for comment.
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