The Welsh side are currently 19th in the Premier League table, having taken just eight points from the first 12 fixtures of the season and have lost six of their last seven league fixtures.
Clement helped the Swans to safety last term after being appointed in January with the club bottom of the league, but now faces pressure himself, with recent reports suggesting that American owners Stephen Kaplan and Jason Levien could replace him with Tony Pulis.
"The owners are very supportive of my position here. The chairman is not happy with the performances, neither am I or the players," Clement told reporters today.
"I see and meet the chairman every day. He's present at the training ground and we sit and discuss all different matters on a daily basis.
"And I have regular conversations with the majority owners Stephen and Jason and all communication remains open and positive."
Next up for Swansea is a home encounter with Bournemouth on Saturday.