"We've got a few little niggles [for Everton]", Shakespeare told a pre-match news conference.
To be a minute away from winning at Old Trafford the other night shows where they are at.
Thirteen of their 21 Premier League encounters have been drawn.
What is the latest Everton team news? Matthew Pennington is likely to come in at centre-back, unless Koeman shifts Mason Holgate into the middle and brings in Jonjoe Kenny at right-back.
Christian Fuchs insists he is enjoying working with Craig Shakespeare and feels the "spark" is back in the Leicester ranks.
However, French midfielder Morgan Schneiderlin could be fit after missing two matches with a calf problem.
Their only defeat in 18 Premier League home games over the past year came against Liverpool in December (W12, D5, L1).
The Foxes have won away just once in the league this season, a 3-2 victory at West Ham on 18 March.
Kevin Mirallas has scored in his last three Premier League games against Leicester City.
Leicester haven't won back-to-back Premier League games away from home in almost a year - a run of three wins in April 2016.
Shakespeare continues to be powerful in turning the winners' fortunes around, with six consecutive wins in all competitions since he took over from Claudio Ranieri easing fears of relegation and taking Leicester into a European quarterfinal. It's helped us win those games.
Asked whether he felt the players had let Ranieri down, Fuchs added: "I always try to give everything". The record is now held by both Pep Guardiola and Carlo Ancelotti (six wins from first six games).
He said: "In this league if you put wins together, especially if you have two games in four days, and you get six points in quick succession you can really push up the table".