Nugent scored his third goal for the club in the 1-1 draw against Lancashire rivals Bolton.
It was just what Burnley needed as the visitors had taken the lead thanks to a superb free-kick from Matt Taylor.
Coyle said: "I speak to David on as daily basis and he enjoys being at the club.
"He feels part of what we are trying to do and there is a smile on his face. There is an energy about him.
"He has all the attributes a striker needs and I feel I could make him an even better player.
"David could have had a hat-trick today. He knows I would love to keep him and my opinion of him.
"I hope we can extend the loan or maybe even sort out a permanent deal as we want to bring young hungry players to the club.
"It is up to the powers that be to sort it out."
Nugent linked up well with Steven Fletcher, although the Scotland striker should have made the breakthrough.
He scuffed a shot wide of the posts from six yards after being released by Wade Elliott.
Burnley though improved in the second half and took their tally to 20 points in their first season since winning promotion to the top flight.
Coyle said: "Fletcher will be disappointed he has not scored but the combination with Nugent is working.
"I felt a little bit aggrieved to be 1-0 down at half-time but Bolton are always a threat at set plays. But then some of our passing and movement was very pleasing on the eye.
"It was just that Jussi Jaaskelainen is a top class keeper and some of his saves were out of the top drawer.
"I thought we deserved to win but we are now on 20 points, which is more than many people thought. What we have to do now is gather more so we can retain our status."
Bolton manager Gary Megson believes Taylor went a long way to answering his critics with his wonder strike.
It was only his fourth goal of the season after he managed 10 in the last campaign.
Megson said: "Taylor bases his game on goals and his ratio of games to goals so far has not been as good as it was last year but he is capable of doing that.
"I was really pleased for him because he has taken criticism this season but he is still brave enough to take that. It was a fantastic strike."
Megson, however, was disappointed at the way Burnley's goal had come about.
He said: "It was sloppy. The ball wasn't whipped in, it wasn't driven in.
"It was well taken by Nugent but from our point of view it was lax and I would expect us to deal with it better.
"There isn't one particular reason why we are not defending so well. The defending has to start from the front as much as your forward play starts at the back. Everyone has to do their job."