The 44-year-old, who had been working as the club's technical co-ordinator, took over as first-team boss on a temporary basis following the sacking of Andre Villas-Boas.
He will take charge of his first Premier League game, away to Southampton on Sunday, after his first match in charge - the Capital One Cup quarter-final tie with West Ham - ended in a 2-1 defeat.
And the former England midfielder, who played for Tottenham between 1999 and 2003, believes he has the qualities to take on the role on a permanent basis.
"If it was down to me I'd be getting a ten-year contract now, but football doesn't work like that," said Sherwood.
"I know all about the football club, I played here, it's my club. I know what the supporters want and I know what they demand, but it's not my decision to make the appointments and we need to respect the men who make those appointments.
"We have to speak long-term with the chairman, it's his decision."
"I'm going to be taking the game Sunday but the games come thick and fast don't they, so I don't know when we're going to fit it in."
The club's technical director Franco Baldini is understood to be keen to bring Frank De Boer to White Hart Lane, although the Ajax head coach appears keen to remain in Amsterdam at least until the end of the current season.
They have also been linked with a move for Southampton boss Mauricio Pochettino, although he has told reporters on Friday that there had been no contact from Spurs, and Swansea boss Michael Laudrup has also ruled himself out.
"I don't think Daniel is linking them to himself, it's the press who are linking the names," added Sherwood. "They are all good guys, good managers.
"The club and the manager have to be compatible, it's not always about the biggest name, he might have done well at another club , he might not do well at this one.
"It's up to the chairman and the board to make the correct decision that's right for the long-term future of the club as it's not good to keep changing managers."
"Tottenham do change managers an awful lot but I am pleased to see Tim Sherwood having a crack at it," he said.
"They have appointed a lot of managers in the past few years but I think the only success they had was with an Englishman.
"So let's hope Tim can get the job, he has great knowledge of the game.
"I hope they don't suddenly think, 'we must get someone because he's foreign.' They have got a boy on their books who knows the game inside out.
"He has been instrumental in helping the likes of (Steven) Caulker and (Andros) Townsend coming through. I would love to see him get the job."
The Tottenham Hotspur Supporters' Trust has demanded answers from Levy about his future plans in the wake of Villas-Boas' departure.
"Following the departure of Andre Villas-Boas on Monday morning and defeat in the Capital One Cup on Wednesday evening, the board of Tottenham Hotspur Supporters' Trust believe it is paramount that the chairman of Tottenham Hotspur Football Club, Daniel Levy, issues a statement addressing the supporters to explain the rationale behind the manager's dismissal and clearly stating his plans moving forward," read a statement released by the trust.
"We believe that now, more than at any time during ENIC's ownership of THFC, the level of frustration and anger being shown by fans renders this request fully warranted.
"As ever, it is made in the best interests of our club."
Meanwhile, Pochettino refused to be drawn on whether he might become Tottenham's next manager.
The Argentinian has impressed since taking over the St Mary's hotseat from Nigel Adkins but insisted he is focusing his attentions on Sunday's clash.
"I am always very respectful with decisions people make at other clubs. It is never good when a colleague is sacked and I want to wish Andre Villas-Boas all the best," he said.
"I never talk about assumptions or rumours. We are fully focused on the game against Tottenham."
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