The former Wales midfielder has reportedly been approached to play the role of former Foxes boss Nigel Pearson.
The Swans have turned their season round recently with Sigurdsson's form pivotal in their renaissance.
Rangers will face Celtic at Hampden Park next weekend.
Aston Villa are on the hunt for a new manager following the departure of Remi Garde.
Hull City are currently in fourth place in the Championship table.
The former Manchester United, West Bromwich Albion and Barnsley shot-stopper has impressed since quitting English football.
The former manager believes the bad atmosphere at the club could be big negative.
The Villans are yet to appoint a replacement for Remi Garde.
Wilson ended a six-month injury lay-off at Aston Villa on Saturday and is keen to finish top of the Cherries' goalscoring charts.
The Clarets netted inside the first minute at Turf Moor.
The Liverpool boss was full of encouragement towards the 19-year-old during first-team training.
Arsenal host Everton at the Emirates in what is sure to be another fine display of football.
The German scored the second against Bayern Munich this week and Wenger is hoping he can find the back of the net more frequently.