The Sun is reporting that Spurs are hoping to complete a deal to sign the 19-year-old, who has been dubbed ‘the next Christian Eriksen’.
The same article states that the Champions League finalists could face competition from La Liga title holders FC Barcelona and Bundesliga giants Bayern Munich.
According to the same story, Tottenham’s Premier League rivals Everton are also interested in the Denmark Under-21 international.
The Sun go on to suggest that a bid in the region of £10m may be required to secure Olsen’s signature in the 2019 summer transfer window.
Tottenham will presumably be hoping that Eriksen’s presence in their squad could prove a persuasive factor if Olsen has a pick of a number of clubs.
Spurs have made big improvements under Mauricio Pochettino in the past five seasons following four successive top-four finishes.
The north London side eased past Ajax on away goals in the Champions League semi-finals to reach their first-ever European Cup final.
Tottenham managed to beat Bundesliga side Borussia Dortmund and Premier League champions Manchester City over two legs before their narrow victory over Ajax.
Spurs finished in fourth place and a point ahead of Arsenal this season.
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