With the Blues facing Manchester City in a titanic midweek clash, Spurs could conceivably cut the gap even further if they can defeat the Swans and Antonio Conte's league leaders fail to record a victory at Stamford Bridge.
Winning in Wales, then, is a must for Mauricio Pochettino's men.
Spurs' win over Burnley was made all the more impressive by their need to completely reshuffle their midfield by half-time.
Harry Winks was stretchered off at Turf Moor after a fairly innocuous incident just before the break and reports suggest that he might have suffered ligament damage, which could well end the impressive young star's season.
Victor Wanyama, meanwhile, sustained a "big injury on his back", according to Pochettino, and both could yet miss out against the Swans.
Erik Lamela remains a long-term absentee but he underwent a successful hip operation recently, with his comeback seemingly under way.
Danny Rose, too, will be absent from this week's encounter as he continues his recovery from a MCL knee ligament injury, while striker Harry Kane is still out due to an ankle problem.
Spurs have no players suspended for the encounter with Burnley.
POTENTIAL TOTTENHAM LINE-UP
Spurs are set to play in their usual 3-4-3 formation, and Son Heung-Min is likely to be asked to deputise for Kane up front after Vincent Janssen struggled against Burnley.
The potential injury absence of Wanyama, however, means that Eric Dier - a goalscorer against Burnley - is likely to be reinstated in central midfield.
However, if Pochettino does not trust the defensive deputies of Kevin Wimmer and Cameron Carter-Vickers, then Dele Alli could drop deeper, with Moussa Sissoko playing further up the pitch.
Kyle Walker is likely to return at right-back after being rested against Burnley, usurping Kieran Trippier.
SWANSEA TEAM NEWS
Swansea are currently mired in a relegation battle and sit just one point clear of 18th-placed Hull City.
The Swans are not likely to be helped by their potential injury absentees, however, with both Nathan Dyer and Angel Rangel certain to miss out.
Talismanic striker Fernando Llorente, scorer of 11 Premier League goals thus far this season, is a doubt after sustaining an ankle injury, while metronomic midfielder Leon Britton could also be unavailable because of a hamstring problem.
BEST OPTA MATCH FACTS
Spurs (26) have won more points in 2017 than any other Premier League team (W8 D2 L1)
Christian Eriksen has been directly involved in nine goals in his six Premier League games against Swansea (5 goals, 4 assists), more than he has against any other side in the competition.
Swansea have never beaten Tottenham in 11 attempts in the Premier League, drawing two and losing nine.
TV COVERAGE & KICK-OFF TIME
The game is due to kick off at 19:45BST on Wednesday but will not be televised live in the UK. Highlights will be aired on Match of the Day on BBC One at 22:45BST.