Jol was Santini's assistant and previously spent 15 years coaching or managing lowprofile Dutch clubs such as Roda JC and RKC Waalwijk.
The 48-year-old, who was in temporary charge for Saturday's-3-2 defeat by Charlton, is adamant he wants the job.
Jol said: "I was always a manager or head coach in Holland and I have been happy here [as an assistant].
"But if you ask me if one of my ambitions is to be head coach or manager, then the answer is yes.
"Frank Arnesen [the club's sporting director] knows my team at every level will play football, nice football."
While Santini's relationship with Tottenham's players was often difficult because of his poor English, Jol is a hugely popular within the squad.
Captain Jamie Redknapp said: "Martin is a very strong character. He comes with a great reputation from Holland. He will be good. With Frank alongside him and Chris Hughton back in the frame, I'm sure we'll be fine in the long term."
Jol joined - along with Santini and Arnesen - as a member of chairman Daniel Levy's continental- style coaching structure. Arnesen believes this structure ensures the club are wellplaced to deal with Santini's departure.
The Dane said: "That is the reason that the board chose to go down that road of having a technical director and then from there on going to appoint the coach and the assistant . It means if something happens, there is always continuity."
