Tottenham are in second place in the Premier League table and five points behind leaders Leicester City.
Spurs have nine games remaining to overturn the five-point deficit and Mauricio Pochettino’s side travel to Premier League strugglers Aston Villa next weekend.
However, former Tottenham midfielder Davids is worried the north London side could end up like Leeds United if Spurs get carried away in the summer transfer window.
“That’s hard to say,” Davids told BT Sport.
“The thing is if you look at it from a long-term perspective, if they go on to be champions, what happens next?
“Because they have to spend regardless. Because you don’t think that the fans are going to think, ‘Okay this one time’. They would want it back to back.
“Then you have to spend, and when you spend three years in a row, you don’t spend well, it can go really like Leeds. That’s the difference and that’s the danger.”
Spurs drew 2-2 with bitter rivals Arsenal in the north London derby at White Hart Lane on Sunday.
Tottenham make the trip to Bundesliga side Borussia Dortmund on Thursday night in the first leg of their Europa League last-16 clash.
Spurs have won six of their last eight Premier League games, hoisting themselves above Arsenal and into second place in the table.
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