Spurs sit 18th in the standings on 34 points with four matches remaining as manager Roberto De Zerbi desperately tries to launch the club out of the relegation zone.
Tottenham could be forced to part ways with several of their key players if they do drop down, with many squad members aiming to jump ship if relegation is confirmed.
With Nottingham Forest and Leeds United sitting five and six points clear respectively of Spurs in the relegation zone, Tottenham must rely on West Ham to drop points.
Speaking on Sky Sports, Carragher admitted that Maddison, who is yet to make a competitive appearance this season after rupturing his ACL, could make a difference if he returns to the side in the final few games.
“Spurs have been really unfortunate with injuries. If they didn't have this injury record they wouldn't be in this position.
“I feel Maddison, who is returning from injury, may have to play a role in terms of keeping Tottenham up.
“He is the only one I can think of in terms of doing something special. He's got that quality I mention in terms of Jarrod Bowen and Morgan Gibbs-White.
“He is coming back from a big injury and we might only be talking about 15 to 20 minutes off the bench, but he is the only one when I look at that squad and think he could produce that little bit of magic Spurs need, especially in the away games at Aston Villa and Chelsea.”
This is the first time in 49 years that Spurs are in the relegation zone this deep into a season (after 33+ league games), since being relegated from the top flight in 1976-77 and if they are to stay up, Maddison could be key to their survival.