Swansea slipped into bottom place in the Premier League at the weekend following the 2-1 defeat to Stoke City at Bet365 Stadium.
Clement, who has been in charge for less than 12 months, looked despondent in his post-match press conference but vowed to fight on in a bid to turn the season around.
He said: "Of course I do (want to be given time). As you know those kind of things are very much out of the hands of the manager or a coach.
"That will always be down to the chairman and the ownership to make those decisions if the situation is going in a really bad direction and you can't see any chance of changing it.
"I believe I can (change it). I showed last year I am capable of working at this level with 29 points over 19 games. It was a big effort, it is nowhere near as good this season. I am the same person, we have a slightly different group of players but the most important thing is to find a way to play better."