Liverpool have long been linked with the duo and have been favourites to sign the youngsters when their contracts expire next summer.
Spurs have already spent £52million on new players this summer, but are ready to further strengthen their squad.
The Mirror reports that Eriksen will cost Spurs around £8million, while Alderweireld will cost the club around £7million.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.