Swansea put their former club captain in charge after they parted company with Michael Laudrup almost three months ago.
The club described Monk's head coaching appointment as being "for the foreseeable future" and speculation has now intensified that he will secure a long-term deal after Swansea's Barclays Premier League survival was secured by their 4-1 demolition of Aston Villa five days ago.
Monk confirmed on Thursday that he has spoken with club chairman Huw Jenkins ahead of the final two league fixtures against Southampton this weekend and Sunderland in 10 days' time.
"We'll see
Of course I am hopeful," Monk said, when asked if he thought he would get the job
"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."
Monk has enjoyed a lengthy career with Swansea, and it would come as a major surprise if he is not handed the reins to take things forward.
Moving clear of the 40-point barrier, though - Swansea currently have 39 league points - is Monk's main objective.
"With everything that has gone on this season, if we get past that total (40 points), no-one can ever question us," he added.
"We've had tough times and we haven't performed as well in certain games, but ultimately we've done our job.
"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."
Source : PA
Source: PA