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  The Foxes beat Hull 3-1 on Saturday and have won both of their games under Shakespeare since Ranieri's sacking.
  "Suddenly he wants to be a manager. It doesn't sit that comfortably with me," Keown said on Match of the Day.
  "If you're assistant manager to Ranieri and he's walked, why is it you suddenly want to be the manager?"
  Shakespeare, 53, has never managed full-time and was brought to Leicester by Ranieri's predecessor Nigel Pearson.
  He says he expects to speak with the Leicester hierarchy about his future next week.
  "You have personal ambition, but I think it's almost out of order that he wants to jump in for that job," said Keown.
  "Surely they'll go for a manager who is bigger with more experience."
  Former Liverpool midfielder Danny Murphy added: "While Craig Shakespeare is winning, leave him in charge. Why change? Let him carry on."
  Speaking after his side moved five points clear of the relegation zone, Shakespeare said: "My remit was to win these two games and that's what we've done," he said.
  "The owners will make a decision for the good of the club and until I talk to them I don't know what that will be. But as I have said previously, I'm comfortable with that.
  "I can't control it and there's no point worrying about it."
  Leicester had not scored a league goal in 2017 until Shakespeare took charge, but have now scored six in two games - twice as many Premier League goals as they did in their last 10 matches under Ranieri.
  Shakespeare has never managed a club before but has a long association with the Foxes.
  The Englishman was assistant manager to Nigel Pearson for two years from 2008, following Pearson to Hull in 2010 before they both returned to Leicester a year later.
  Following Pearson's sacking in 2015, Shakespeare remained at the club as Ranieri's assistant.
  Leicester are believed to have spoken to a number of potential candidates to replace Ranieri, but could also consider giving Shakespeare the job until the end of the season.
  The Foxes have held informal discussions with former England boss Roy Hodgson.
  The 69-year-old has been out of work since leaving the international set-up after the Three Lions lost to Iceland at Euro 2016.
  Pearson, who saved Leicester from relegation in 2014-15, has also been linked with a return.
target: Leicester City caretaker boss Craig Shakespeare is "out of order" for wanting to replace Claudio Ranieri, says ex-Arsenal defender Martin Keown.