Asked who he thought might become manager, Pleat said: "There are greater pressures than ever but I am glad to say that question needs to be directed to the chairman.
"He will deal with it successfully in time. It is one decision that I am not involved with although I have been very close to everything that has gone on.
"I think they are closer (to an appointment) than they were. We had a setback during the season on the decision-making process but they are closer than they were."
That setback was clearly a reference to the on-off saga to appoint Giovanni Trapattoni. Spurs believed they had an agreement earlier this year with Italy's national coach to join the club on 1 July and wanted to announce it during January to put an end to the speculation.
But Trapattoni twice pulled out of talks over concerns that his wife would be homesick.
Levy paid tribute to Pleat for his work during his six-year association with the north London side, saying: "I should like to thank David for his contribution to our club over the years.
"I think it is too easy in the business of football to forget to give credit where it is due and David has brought young players to this club who have gone on to establish themselves in the first-team squad.
"This decision is the result of a major review and it would be wrong to align it simply to this last season when David took over as caretaker manager.
"Frank's knowledge of the international transfer market is excellent and no club can operate without that in today's market place.
"He has a proven track record of working successfully alongside some of the world's top managers. The appointment of our first-team management progresses as before and will be announced in due course."
