Lyn Jones left by mutual consent after "a period away through illness".
Kingsley Jones is in charge until the end of the season and takes them to Montpellier for Saturday's European Challenge Cup semi-final.
"I'm totally open-minded to be honest. The big thing for me is the next four weeks," Kingsley Jones told Scrum V.
"I've really got to focus on that, make sure we get as much out of this season as we can and hopefully we get to a final, which would be fabulous."
The former Wales flanker insists Lyn Jones, another ex-Wales open-side, was ill before his departure from Rodney Parade was announced.
"You've got to take it as read," said Kingsley Jones.
"There was a process. Lyn was ill, there's no doubt about that and as it said in the statement, it's two parties that probably think it's time to move on.
"OK, yeah, it could have waited until the end of the season, perhaps, and ultimately often when you're in this position someone's going to move on, it happens immediately.
"They've parted ways and I'm sure Lyn will go on to great things, whatever he decides to do.
"He's worked really hard in the last three years and I don't think the guy's had a day off."
Newport Gwent Dragons head coach Kingsley Jones is "open-minded" about the possibility of succeeding Lyn Jones as director of rugby.