The Argentine recently took charge of Spurs following Tim Sherwood’s sacking, and is thought to have major plans in the transfer market as he plots to move the London club back into the top four.
An area of priority is believed to be left-back, with the Lilywhites possessing few options in the role.
Danny Rose is the club’s only orthodox choice, and his injury woes last season exposed a lack of depth, with Jan Vertonghen – a centre-back by trade – forced to fill the void.
Davies is seen as a wise buy by Pochettino, who has been impressed by his rise through the ranks at the Liberty Stadium in recent seasons.
Swansea are keen to keep their starlet, but the cash on offer could be tempting for Garry Monk as he plots his own moves.
The South Wales club already have a ready-made replacement in the shape of Neil Taylor.