While the pair were not thought to be initially in the running for the job, chairman Phil Gartside has been impressed with the work that they have done so far, according to The Guardian.
Lee, who had a spell in charge of Wanderers back in 2007, has admitted that he and Phillips have so far enjoyed their stint at the helm.
"These last few days have been fantastic, but I've thoroughly enjoyed my time since I have been back here, if I'm being honest," he told the club's official website. "When Jimmy and I were asked to do it, we didn't give it a second thought. I will do whatever I can for the football club.
"The boys have been spot on. They have been focused and I have been very pleased with their application. We know there is a lot of quality in that dressing room.
"We have a gameplan which we want to impose on whoever we play, but in order to do so you have to have the basics right. We have been working hard on that and have stripped things back."