The north London duo are both believed to be keen on the Spaniard, and were even rumoured to have made tentative approached regarding a deal for his signature during January.
These were rebuffed, with Atletico hopeful that he would rediscover his goal scoring touch.
The 25-year-old enjoyed a fine 2011/12 season at the Vicente Calderon, netting an impressive 19 times in all competitions.
But, this term he has struggled, producing just four goals across all competitions.
This form has frustrated the Atletico, who are new believed to be willing to sell up whilst Adrian’s value is still fairly high.
Spurs are known to be desperate for attacking additions, with manager Andre Villas-Boas having only Emmanuel Adebayor and Jermain Defoe to call upon.
Meanwhile their local rivals are also in the chase, as they look to build a squad capable of competing for silverware next season.
The duo could face competition from Liverpool and Everton, with the Merseyside pair also believed to be monitoring the situation.
Adrian joined Atletico from Deportivo La Coruna in 2011, following the club’s relegation to the second tier of Spanish football.
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