The Spaniard has been heavily linked with Chelsea and RB Leipzig, while Manchester City and Manchester United have also been mentioned as potential suitors.
However, Mundo Deportivo say Spurs have agreed personal terms with Moriba, but they have yet to make contact with Barca about the transfer fee.
It is believed that the Catalan club are holding out for a figure in the region of €20m (£17m) for the 18-year-old, despite the fact that he could leave on a free transfer next year when his contract expires.
TMW also report that Tottenham are “best positioned” to complete the transfer, despite both Chelsea and Leipzig having held talks about signing the teenager in “recent days”.
Moriba’s future could well be decided by who is prepared to match Barcelona’s asking price before the transfer window shuts next week.