Spurs are battling a host of clubs for the talented playmaker, who could become an ideal deputy for Christian Eriksen.
Maddison would on one level be a fine addition, but paying £20 million for him would be an admission of failure from Tottenham.
Spurs were eyeing him up two years ago when Maddison was at Coventry City.
Days later at the January transfer deadline, Norwich City stole in to sign Maddison.
It was bizarre for Tottenham to let this go through unchallenged considering their success with Alli a year earlier, and the scouting work done with regard to Maddison.
Paying £20 million for him now would be an uncharacteristic admission of failure by Spurs chairman Daniel Levy.