And it is understood that Davies, 21, is keen on a move to White Hart Lane.
A deal was agreed in principle for the Wales international last month but Swansea chairman Huw Jenkins pulled out of the arrangement in search of a better offer.
But despite reported interest from Liverpool, Spurs remain determined to capture Davies - a key target for new manager Mauricio Pochettino - and opened fresh talks over a possible sale.
Davies became a regular for Swansea during the 2012-13 season following long-term injury to defender Neil Taylor, and he excelled under both previous manager Michael Laudrup and current boss Garry Monk.
He has made 71 appearances, signed a one-year contract extension last year and has gone on to make 10 caps for Wales.
Tottenham, who are the only Premier League club yet to make a signing in the current window, are in need of a left-back, with centre-back Jan Vertonghen filling in for the injured Danny Rose for large periods of last season.
Davies is currently part of Swansea’s pre-season tour of the USA and played 45 minutes in the friendly draw with Chivas Guadalajara on Wednesday.
Spurs are currently in Seattle having touched down in the US on Thursday ahead of their first pre-season schedule.