He said: "I know exactly who I want to lead this club next year. I have every confidence he will arrive here in the summer."
Martin O'Neill, Alan Curbishley and Graeme Souness have all been linked with the job.
Asked specifically about O'Neill, Levy said: "It's natural that Tottenham is going to be associated with lots of good managers. Martin's a good manager but he's one of many good managers."
Despite Pleat's stop-gap status and the £12million Spurs spent last summer, Levy has not ruled out signing new players.
He said: "If appropriate opportunities are available we will consider them. The amount of money we spent last summer was second only to Chelsea and is not something which is sustainable - you can't really spend more than you earn, but we will continue to invest in new players."
Tottenham would have more cash at their disposal if Joe Lewis - the Bahamas-based billionaire behind the club's largest shareholder Enic - became more actively involved.
However, Levy dismissed suggestions that Lewis could emerge as Spurs' answer to Roman Abramovich.
He said: "Mr Lewis continues to be a supportive investor but we will not see the sums of money invested that Chelsea have at their disposal." Levy also refuted claims that Abramovich had talked to officials about buying Spurs before settling on Chelsea.
He said: "We have not had any discussions with any individuals interested in buying the club."