Spurs finished in fourth place in the Premier League despite being without England international Harry Kane for the final months of the season.
Tottenham managed to get across the line thanks in part to the abysmal form of their top-four rivals Arsenal and Manchester United.
The north London side have the Champions League final against Liverpool FC to look forward to next month after Spurs came from 3-0 down to beat Ajax on away goals.
Kane netted 17 times in 28 games in the Premier League this season, while South Korea international Son Heung-min chipped in with 12 goals.
Former Liverpool FC defender Thompson believes the north London outfit need to sign a new striker in the summer to support Kane next term.
“I think they need a bit of strengthening all around, maybe in the full-back areas. There is talk of Christian Eriksen leaving, who is their creative influence. That would be a big blow to Tottenham,” Thompson told Sky Sports.
“I think Fernando Llorente could move on too as he will want more game time, so it is similar to Liverpool – they will need a decent forward to work alongside or perhaps off Harry Kane. They need to beef up the quality of their squad. They have 14/15 that are decent but they must bulk up with quality rather than quantity.”
Tottenham will take on Liverpool FC in the Champions League final in Madrid next month as Spurs look to win the competition for the first time.
Spurs have never got their hands on the Champions League trophy, and their best previous run saw Tottenham reach the quarter-finals in 2013.
Tottenham managed to beat Borussia Dortmund, Manchester City and Ajax en route to the final.
Their opponents Liverpool FC lost 3-1 to Real Madrid in the Champions League final last term.
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