"I can't see why not, but it's the chairman's decision," Simpson told British media 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."
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Simpson joined striker Jamie Vardy, goalkeeper Kasper Schmeichel and winger Marc Albrighton in playing down media reports suggesting a player revolt led to Ranieri's dismissal.
"It's not nice to hear that. The chairman is his own man and he makes his decisions. All we have to do is play football," the 30-year-old said.
"We know we haven't played how we can - we're first to admit that - but we have to carry on. Leicester carries on."
Leicester, who are 15th in the league table with 12 games remaining, host Hull City on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Amlan Chakraborty)
