Monk was placed in charge at the Liberty Stadium almost three months ago when Michael Laudrup was relieved of his duties.
His appointment was described as being 'for the foreseeable future' and speculation has intensified Monk will be told to carry on after securing the club's Premier League future with a 4-1 win over Aston Villa last weekend.
He revealed talks had taken place with chairman Huw Jenkins but now has to wait until the end of the season to learn his long-term fate.
"We'll see. Of course I am hopeful," said Monk, when asked if he thought he would get the job at his press conference ahead of Saturday's home clash with Southampton.
"It is something I really enjoy doing, I've learnt a hell of a lot in a short space of time, and once you get a taste of it you don't want to let it go.
"I trust the board and the chairman and everyone that they will make the right decision for the club.
"I have spoken to the chairman. It was a review of what I have done this season and stuff like that, and going forward, how I feel about things and what I would do. You would have that chat anyway.
"We just had a general chat, a chat on how the season had gone, the things I had gone through, what I thought about the future and what he thought. I think there is a board meeting planned before the end of the season when they will chat and discuss things and make a decision.
"I said at the start of all this that I would do it properly. I would do it as if I am planning for the future and taking the club forward.
"I think if I wasn't doing that, it wouldn't put me in a good situation. I have spoken to the chairman about the future, possible targets, positions you would want to strengthen within the squad.
"I've said from the start that what I want from when a kid walks through the door, from five or six years old to the first team, is that everyone understands what it means to play for this club and what it stands for.
"The main thing for me is that everyone understands that when they put that shirt on what they are representing. I can only give my views on the club, which I gave to Huw, and they have to remain between me and Huw."