Leicester ended their five-game losing streak in the Premier League with an emphatic 3-1 victory over Liverpool in Shakespeare’s first game in charge since Claudio Ranieri’s sacking.
Shakespeare, 53, is expected to take charge of the champion’s visit of Hull on Saturday (3pm) as the Leicester board continue their search.
“I can’t see why not, but it’s the chairman’s decision,” Simpson said when asked of Shakespeare’s chances of landing the role on a permanent basis.
“It’s up to him and he owns the club, he is passionate about the club.
“Those decisions are nothing to do with us but, for me, (Shakespeare) has been really good. He is a top coach, a top guy and he has taken it on naturally.
“He has kept it simple and told us what he wanted to do and we’ve done that so let’s hope we can carry it on for him.”
Simpson also joined Jamie Vardy, Kasper Schmeichel and Marc Albrighton in playing down media reports suggesting a player revolt led to Ranieri’s dismissal last Thursday.
“It’s not nice to hear that,” the 30-year-old added. “The chairman is his own man and he makes his decisions. All we have to do is play football.
“We know we haven’t played how we can – we’re first to admit that – but we have to carry on. Leicester carries on.”
