Although the Swans beat Newcastle away last weekend - a victory that took them six points above the relegation zone with only three games left - Monk believes there is still work to be done.
The 35-year-old former Swansea captain was put in charge following manager Michael Laudrup's Liberty Stadium exit almost three months ago.
Whether he keeps the role beyond this season remains to be seen, but Monk insists his sole focus is seeing Swansea maintaining their top-flight status.
"We are not secure
It's not mathematically done yet," said Monk, ahead of Saturday's clash against Aston Villa.
"When that comes about, I am pretty sure that is when I will be able to sit down with the board and see what the future is.
"The future for me was always to go into coaching and management
Who wouldn't want to do a job like this?
"If we go into these (last) three games and we don't get any points and the other teams win, then we are relegated
It's far from over for us.
"When it is mathematically done, that is when I can sit down with the chairman and the club and see what the future is and what their thinking is.
"I can only do what I am doing
My job is to keep the club in the league, and we are nearly there, but it is still on us to make sure that we complete the job.
"In terms of my future, until that day is done, I don't care about myself
When that day is done, that's when I will start to think about myself and what the future is for me and also for the club."
Swansea will go into the home game against Villa without Spanish striker Michu, whose injury-hit season shows no sign of abating.
He was sidelined for three months due to an ankle problem, and although he subsequently returned to action, ankle swelling is now keeping him out.
"We can't quite seem to get the swelling down," Monk added
"It's really small margins.
"Along with our medical department, he has travelled to Spain to see the national doctor for information from him
We will know more today.
"The bottom line is he just needs that rest
That is the only way you really get over these injuries
All players play with all types of injuries, and the only real cure is rest.
"He will be out for the weekend, and we will see how it progresses next week.
"We have to be careful
As much as we want him to play, and he wants to play in the remaining games of the season, the bigger picture is he is an important player for the club
It is important he gets that rest and he comes back as strong as ever.
"I know how frustrated he is, but if it means him resting to come back strong and fit ready for next season for Swansea, which is the most important part, we will have to do it.
"He is a big player for us, let's not make any bones about that
He scores a lot of goals, he is a quality striker, a very good player and a good character in the changing room."
Source : PA
Source: PA