The Swansea City left back's preference is to be reunited with Brendan Rodgers at Anfield this summer, with the Reds prepared to meet the Welsh club's asking price.
Though Spurs are understood to have agreed to a fee and are prepared to pay more for the youngster up front, the Reds are ready to meet the Swans' 12.5 million-euro asking price.
Davies' preferred destination is Anfield, with the prospect of Champions League soccer a big draw as well as working with former Swansea boss Brendan Rodgers in a team that nearly won the Premier League in 2013-14.
Tottenham's interest in the left back, who has had the better of his battle with Neil Taylor for a place in the Swans' first team, was confirmed by the Welsh club's chairman, Huw Jenkins, earlier in July.
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But Spurs, who are the only Premier League team yet to complete a signing so far this summer, are likely to be beaten out by big-spending Liverpool. The Londoners are continuing their attempts to persuade Davies to move to White Hart Lane but fear that even a guaranteed starting role will not be enough to change his mind.
With the return of Champions League soccer to Anfield and the 88 million-euro sale of Luis Suarez to Barcelona, Rodgers has already spent close to 75 million euros on Adam Lallana, Rickie Lambert, Emre Can and Lazar Markovic.
The pursuit of Davies is part of a defensive recruitment that also includes a move for Southampton center back Dejan Lovren.