The 30-year-old Netherlands international has been granted permission to speak to Spurs via his representative after the Premier League clubs agreed a fee over the weekend, thought to be in the region of £5million.
The proposed deal is complex and dependent to an extent on a separate agreement for left-back Ben Davies to join Spurs and for midfielder Gylfi Sigurdsson to move in the opposite direction.
Negotiations concerning all transfers are thought to be going well, but Vorm has reservations about how much playing time he will get in competition with current Tottenham and France No.1 Hugo Lloris.
Lloris, 27, recently signed a new five-year deal at Spurs, but Europe's top clubs are becoming increasingly keen to have two top-class goalkeepers battling it out for the No.1 spot and Tottenham are no exception.
Vorm is an experienced Dutch international and Premier League regular with Swansea, whom he joined from Utrecht in 2011, and Spurs believe he would strengthen their goalkeeping department.
Tottenham's other established keeper is the 43-year-old veteran Brad Friedel, who also signed a one-year contract extension this summer.
However Friedel, a former USA international who played in the 3-3 pre-season friendly draw with Seattle Sounders on Saturday, is expected to take on a more senior, coaching role alongside new goalkeeping coach Tony Jimenez, as well as providing first-team back-up.