Premier League champions Leicester have held informal talks with former England boss Roy Hodgson about him becoming their new manager.
However, it is thought the 69-year-old was just one potential candidate spoken to in the search for Claudio Ranieri's replacement.
And acting boss Craig Shakespeare could stay in charge until the end of the season if results continue to improve.
Ranieri was sacked on 23 February, nine months after winning the title.
The Italian departed with the Foxes just one point above the relegation zone.
Shakespeare's first match as caretaker manager resulted in a 3-1 victory over Liverpool on Monday.
Defender Danny Simpson said Shakespeare is a "top coach and a top guy".
He said: "He has kept it simple and told us what he wanted to do, which was simple and basic, and we've done that so let's hope we can carry it on for him."
'Public perception of Hodgson is totally wrong'
Hodgson has been out of work since resigning as England coach after they lost to Iceland at Euro 2016.
But his former goalkeeping coach Dean Kiely says Hodgson should be a leading contender for the Leicester job and the public perception of the veteran manager is "totally wrong".
Kiely, who worked under him at West Brom, said: "I can see why he's on anyone's shortlist."
He took the Three Lions to the quarter-finals at Euro 2012, but two years later they were eliminated at the group stage of a World Cup for the first time since 1958.
Hodgson's team won all 10 matches in qualifying for Euro 2016 but he quit after a 2-1 defeat by Iceland in the last 16 left him with a record of three victories from 11 games in major tournaments.
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Former Republic of Ireland goalkeeper Kiely told BBC Radio 5 live: "The public perception is totally wrong to how he is as a person and how the players react to him, which is only positive from my point of view.
"The end of his England reign was quite negative but shouldn't wash away all the good work he had done in the campaign leading up to that and also his club management career, certainly at West Brom."
Kiely said Hodgson "brought stability" when he succeeded Roberto di Matteo at The Hawthorns in February 2011.
"He was great," said the former Charlton goalkeeper. "He just wants to be out on the training ground, with tracksuit on and coaching the players.
"I was fortunate to go in for England training when Roy invited me in. On the grass, he comes alive and the best thing for me was the players responded great to Roy.
"He's a fantastic fella away from football also, very engaging, and the time I spent with him was excellent for me. I learned a lot."