Sherwood took over from Andre Villas-Boas in December and immediately brought Adebayor back into the fold.
The 30-year-old has 13 goals in all competitions since regaining his starting berth under Sherwood, with 10 coming in the Premier League.
Sherwood's position has regularly been called into question with the likes of Ajax coach Frank de Boer linked with the hotseat at White Hart Lane, however Adebayor has reiterated his desire for the manager to stay.
"Hopefully he stays, but I am not the chairman of the club so I can't tell you anything about that," he told The Tottenham Journal.
"We will see what happens in the future.
"No matter where he goes, I will always keep him in my heart and I have a huge respect for him - as a manager, as a friend, as an ex-footballer, because he knows what it takes to be a footballer.
"He respects everyone equally, and for me he is a great man and a great manager."
Adebayor's impressive numbers come despite not featuring regularly under Villas-Boas, with the former Arsenal forward targeting a more positive campaign next season.
With Sherwood's potential departure putting a question mark on Adebayor's future at the club, he said he is eager to stay settled and recapture his best form.
"I just want to forget the bad moments and look to the good ones and the good games I have played and learn from, and work hard for the next season," he added.
"Hopefully I will have a proper pre-season, because for the last three years I haven't had one. It's very difficult for a player not to have a pre-season.
"I have the quality and a big belief in myself. I know I can do it and I will do it.
"The last three or four months have not been that bad, there are a lot of positives to take out of it, and we just have to learn from our mistakes and keep going."
