The Championship side are keen to bolster their options at full-back following their relegation from the Premier League.
Spence is third in the pecking order at right-back behind both Pedro Porro and Emerson Royal.
Both have started ahead of the 23-year-old in Tottenham's opening two matches this season.
Spence was a standout during the 2021/22 campaign while on loan at Nottingham Forest from Middlesbrough, netting twice whilst setting up five.
He also helped Steve Cooper's side seal promotion from the Championship, which prompted Spurs to sign him.
read more on leeds
James Maddison recommends unsettled Leicester player to Leeds boss Daniel Farke
Leeds confirm Tyler Adams transfer to Bournemouth in 18 word statement
The defender is now expected to drop down a league, with Daniel Farke's side keen.
Leeds are without regular left-back Junior Firpo, who is sidelined through injury.
Luke Ayling can play on the right, but the club are keen to bolster their backline further.
Former Norwich star Sam Byram has already re-joined his boyhood club on a free transfer this summer.
Most read in Championship
Smith Rowe offered to rival, Chalobah latest, huge Salah contract, shock Man United move
Arsenal star offered to Premier League clubs following Chelsea transfer approach
Thomas Tuchel pushing to bring Chelsea defender to Bayern Munich this summer
Premier League club look to hijack Tottenham's move for Brennan Johnson with record offer
Leeds are also eyeing a move for Leicester left-back Luke Thomas, as talkSPORT previously revealed, following the recommendation of James Maddison.
The 22-year-old has fallen out of favour at the King Power Stadium and is expected to leave before the transfer window closes on Friday.
Maddison, who left relegated Leicester to join Tottenham in June, knows Farke well from his time playing under the German at Norwich.
He's yet to feature for Leicester under Enzo Maresca, despite returning to the club as a winner of the Under-21 European Championship with England in the summer.
Leeds have conceded seven times in just four matches, having endured a mixed start to the new season.
The Whites managed a 4-3 victory away at Ipswich last weekend and face bottom-of-the-league Sheffield Wednesday on Saturday.
CSKA Moscow 
Akhmat Grozny 
Newcastle 
Manchester City 
Udinese 
Inter 
VFL Wolfsburg 
VFB Stuttgart 
Lokomotiv Moscow 
Spartak Moscow 
Arsenal 
Leicester 
Chelsea 
Brighton 
Everton 
Crystal Palace 
Willem II 
PSV 
Dnipro-1 
Dynamo Kyiv 
Genoa 
Juventus 
Wolverhampton 
Liverpool 
Bayern Munich 
Bayer Leverkusen 
Real Sociedad 
Valencia 
NEC Nijmegen 
Feyenoord 
ST Johnstone 
Celtic 
Bordeaux 
Metz 
Monaco 
Montpellier 
Osasuna 
Barcelona 
Benfica 
Gil Vicente 
Torino 
Lazio 
Rangers 
Hibernian 
Toulouse 
Lyon 
Roma 
Venezia 
Modena 
Sampdoria 
Holstein Kiel 
Eintracht Frankfurt 
Athletic Bilbao 
Sevilla 
Waalwijk 
Ajax 
Manchester Utd 
Tottenham