Steve Walsh and director of football Jon Rudkin were both reported to be in attendance, with Ilicic the reason for their trip.
The Slovenian international has been impressive for Fiorentina this season, scoring 14 goals in total, 12 in Serie A and a further two in the Europa League.
The 28-year-old can play up front or behind the striker, and was just last week linked by The Star with a move to Liverpool.
Leicester's win at the weekend and Manchester United's loss to Tottenham meant the Foxes have secured Champions League football for 2016/17, whatever happens with their title bid.
This gives him a huge lift in income, and with clubs also hovering to try and sign their top stars, they will need to be active in the transfer market to strengthen, and ensure that if one or two key players do leave, they are ably replaced.
Ilicic is a player with international experience, who has played in Italy since 2010 when he joined Palermo, and could prove to be a shrewd addition to their attack.