Leicester remain in talks with Dean Smith with a view to a short-term appointment as manager.
The 52-year-old is a serious option to replace Brendan Rodgers until the end of the season, the PA news agency understands.
Smith is one of a number of contenders the Foxes have spoken to, having seen a move for former Leeds boss Jesse Marsch collapse over the weekend.
The pair worked together at Carrow Road and Villa while Shakespeare had a brief spell as manager at the King Power Stadium in 2017, having been assistant to Claudio Ranieri when the Foxes won a stunning Premier League title in 2016.
Nothing has been completed yet, with Adam Sadler and Mike Stowell having taken caretaker charge of the last two games.
Leicester, who have lost eight of their last nine matches, reluctantly sacked Rodgers last weekend with the club second bottom of the Premier League.
They suffered damaging home defeats to Aston Villa and Bournemouth last week and go to Manchester City on Saturday.