After a sluggish start under new boss Paulo Sousa, the Swans are now in the thick of the play-off places and have lost just one of their last 10 games.
With just over a third of the season remaining, Monk knows only hard work will see his side achieve their target.
"I will be saying to all the boys that we have got three or four months ahead of us which could change all our lives forever," Monk told the Evening Post.
"We all want to play at the highest level and the fact is we have a chance to do it together with Swansea City. It's a big ask, I know, but we have worked hard to get where we are and we don't want to waste the position we're in.
"If we do get to the Premier League, I think we'll have earned it."
Source: PA
Source: PA