Jose Mourinho's side will be the favourites to progress, but Boro will enter the third-round clash off the back of four straight Championship victories.
Sunday's clash will actually be the first time that these two teams have locked horns since February 2017, when Spurs recorded a 1-0 victory. Tottenham have won each of their last three clashes with Boro, who have not overcome the London club in any competition since a 2-1 success back in August 2008.
Boro have never won the FA Cup, but they did reach the final back in 1997, while their head-to-head record against Spurs is won 35, drawn 23 and lost 35. What's more, Jonathan Woodgate's side will enter the match full of confidence following an excellent run of results in the second tier of English football.
It has been a difficult season to date, and the Riverside club are still only 16th in the Championship table, although they have beaten Stoke City, Huddersfield Town, West Bromwich Albion and Preston North End during a fine run.
The league is most important for the club this season as they look to move closer to the playoff spots, but the chance to progress to the fourth round of the FA Cup at Tottenham's expense will be extremely enticing.
The club's January has also got off to a positive start in terms of signings, with Patrick Roberts and Lukas Nmecha joining on loan from Manchester City. Both players trained with the club on Friday and will be in contention to make their debuts in the clash with Mourinho's side.
There has been a lot of talk surrounding whether Spurs can end their long wait for a trophy under Mourinho this season. They will not be winning the Premier League this term, while it is difficult to imagine them making a serious play for the Champions League despite reaching last season's final.
As a result, the FA Cup potentially represents their best chance of silverware. It is a competition that the club have won on eight occasions, with their last success coming in 1991. The capital outfit have not lifted a single trophy since the 2008 League Cup, though, which is too long for a club of their ilk.
Tottenham have picked up some strong results since Mourinho replaced Mauricio Pochettino as head coach, but they will enter this match off the back of two disappointing results in the Premier League; first sharing the points with Norwich City before losing at Southampton on New Year's Day.
As a result, Spurs are sixth in the Premier League table, six points off fourth-placed Chelsea. Securing a top-four spot is far from a lost cause, although their inconsistency could prove to be a real problem in the coming months.
Tottenham's next Premier League game is actually at home to runaway leaders Liverpool next weekend, and Mourinho will be desperate to enter that match off the back of a positive result in the FA Cup.
Middlesbrough form (all competitions): DLWWWW
Tottenham Hotspur form (all competitions): LWLWDL
Woodgate confirmed at Friday's press conference that new signings Roberts and Nmecha could both be involved at the Riverside, although it seems unlikely that either player will start.
Rudy Gestede and Ashley Fletcher are also set to continue in the final third of the field, although Darren Randolph, Marcus Browne, George Friend, Ryan Shotton and Anfernee Dijksteel are all still injured.
It seems likely that Son will return to the team, while Lucas Moura could lead the line in the absence of Kane, whose fitness will be monitored in the coming weeks as he attempts to overcome his hamstring issue.
Middlesbrough possible starting lineup:
Pears; Howson, McNair, Fry; Spence, Wing, Saville, Coulson; Tavernier; Gestede, Fletcher
Tottenham Hotspur possible starting lineup:
Vorm; Aurier, Foyth, Sanchez, Sessegnon; Winks, Sissoko; Son, Lo Celso, Lamela; Lucas
We say: Middlesbrough 1-2 Tottenham Hotspur
Boro are more than capable of picking up a positive result this weekend, and the home side will enter the match in the better form. Spurs are due a win after two disappointing results, though, and we fancy the Premier League side to progress to round four courtesy of a narrow success at the Riverside.