Spurs have made signings this summer, but have not yet landed a centre-back, despite that being a priority.
They could even see central defenders leave, with Davinson Sanchez attracting interest, while Japhet Tanganga also has admirers.
However, with the new season fast approaching, the Lilywhites have put the onus on making progress in the transfer market and in the centre-back hunt.
Fulham’s Adarabioyo, who has been on their shortlist for some time, is now a player that Tottenham will move for and it is claimed they will put in a bid this week.
Tottenham have also held discussions with Bayer Leverkusen for Edmond Tapsoba and with Wolfsburg for Micky van de Ven but have failed to make headway.
Adarabioyo also has interest from Ligue 1, where Monaco are keen.
The former England Under-19 international, who has less than a year remaining on his current contract, featured in 25 league games for Fulham last season.