The news comes in the wake of speculation that manager Michael Laudrup's future at the club may be in doubt after Saturday's loss at West Ham left Swansea just two points outside the relegation zone.
Laudrup is 4/7 favourite in Sky Bet's 'Next Premier League boss to leave' market and Monk's price to be the next manager of the club has been trimmed dramatically, following the news that he will take a coaching post.
Sky Sports reporter Graham Thomas said: "Sources have suggested to me that Garry Monk will be joining the Swansea City coaching team to work underneath Michael Laudrup.
"I think this decision has come from the board, led by chairman Huw Jenkins.
"Monk is one of the longest-serving players in the Swansea squad, he's been at the club for most of the past decade.
"He has hardly played this season because he has lost his place to Chico Flores and he has also suffered injuries but the concern among the Swansea boardroom is that the team have been allowed to drift in recent weeks.
"Michael Laudrup has cut a rather distant, withdrawn figure and Monk, who is a very well-respected voice of authority within that dressing room, is seen as the ideal figure to get things back on course.
"I managed to get a brief word with Michael Laudrup earlier and, when I asked if he was staying at the club, he replied 'Well, why wouldn't I?'
"At the moment, Garry Monk is coming in to work alongside Michael Laudrup."
Cardiff are 19th in the Premier League table but lie just three points behind Swansea in 12th and Laudrup's team play host to their rivals in a critical south Wales derby on Saturday evening.