The Swans only need to draw at Newcastle on Saturday to set a new club points record in the Premier League but Monk wants to achieve more than that with five games of the season remaining.
Swansea currently lie in eighth place on 47 points and Monk’s ambition is for them to finish top of what many observers would consider the “best of the rest” with the top seven in the table having pulled clear.
“Considering everything, top 10 is a fantastic achievement – or it could be a fantastic achievement,” Monk said.
“It would be extremely disappointing if we finish outside it now but the greedy side of you wants more.
“Ninth place is the best we’ve finished but to beat that and finish in eighth in that mini-league in the middle with Stoke, Palace, Everton, West Ham… it would be great to finish on top of that.
“It has to be part of the motivation and something I will remind the players as well.”
Swansea, who were tipped for relegation in some quarters at the start of the season, missed out on their first opportunity to beat the 47-point mark last weekend when they lost 2-0 to Leicester, who were bottom of the league at the time.
“I put it to the players at the start about beating the club’s points record,” Monk said.
“I knew I could get the players committed to the work to get ourselves in this position, that is easy to say now but I truly believed with the quality we added in the summer to what we had then we could do something.
“We knew people would say we would struggle and the manager does not have enough experience, but I I knew we could get to this point.
“But the most important thing is we finish it off what we have started and not just crawl across the line.
“It is a five-game period which could define our season in terms of how it is looked upon when it really shouldn’t be like that. I am aware of that and it is about making the players aware of that.”