The 21-year-old Albion winger was taken to the Scottish giants on loan in January by Rodgers, who has subsequently left for Leicester City.
But Burke, who has four goals from eight Scottish Premiership games, is still enjoying his time in Glasgow and relishing the chance to work with caretaker boss Neil Lennon.
“Personally I’m still happy here,” he said. “I’m enjoying my football. It’s a massive club with great fans and great people.
“I don’t think it (Rodgers’ departure) changes anything. I’m very happy. As long as I’m playing football and enjoying myself I don’t care who the manager is.
“I wouldn’t say I was disappointed that Brendan has gone. I still feel I can learn a lot from the new manager and I’m looking forward to working under him.
“I’d never met him before but he seems really good, really passionate about the club. He knows what it’s all about so he’s the right man for the job.”
Burke has been a big hit north of the border, and has hinted at a potential permanent stay at Celtic.
He’s struggled for minutes at Albion and has only scored one goal for the Baggies since his £15million move from RB Leipzig in the summer of 2017.
But the 21-year-old still has more than three years left on his Albion contract and Darren Moore insists he has a future at The Hawthorns.
“I’m sure we’ll see the player we’ve invested in when he gets back,” said Moore, this year. “He’s a tremendous player, he just needs the volume of games. If he gets that we’ll see a great player for West Brom.
“I’m developing Oli because of the output we’ve laid on him. We’ll get him back in the summer and have a player who’s nearer the front line than just playing bit-parts.”