McNeill had suffered from dementia for a number of years.
Rodgers has been linked with the position at the King Power Stadium since Leicester sacked Claude Puel.
Celtic were 2-0 up early in the second half when they put the ball out of play to allow treatment to their midfielder Ryan Christie.
Arsenal will now avoid any of the Champions League drop outs in the draw for the next round as they have a better head-to-head record with second-placed Sporting Lisbon.
Celtic beat Dundee 5-0, while in a game against Hearts, Hibs coach Neil Lennon was struck by a coin.
Aberdeen beat Rangers 1-0 to reach the Scottish League Cup final, where they will play against Celtic.
Hearts beat Aberdeen 2-1, while Celtic also won their match, beating Hibernian 4-2.
Australia coach Graham Arnold intends to give Celtic midfielder Tom Rogic an expanded role within the national team.
James Forrest scored four goals as Celtic thrashed 10-man St Johnstone 6-0 to record their first away win in the Scottish Premiership this season.
Leigh Griffiths scored the winning goal as Celtic beat St. Johnstone 1-0.
Steven Gerrard's Rangers team beat St. Johnstone 5-1 to overtake Glasgow rivals Celtic.
Stuart Findlay's header gave Kilmarnock the victory over Celtic.
In Rangers coach Steven Gerrard's first Old Firm derby, Celtic came out on top, winning 1-0.
Celtic accepted Lyon's offer of £18 million for Moussa Dembélé.
Sevilla, Celtic, and Rangers all won or drew their Europa League playoff matches, while Burnley lost to Olympiakos.
AEK Athens and PAOK beat Celtic and Spartak Moscow respectively to advance to the Champions League playoff round.
In Champions League qualifiers, Celtic drew 1-1 against 10-man AEK Athens, while PAOK Salonika came back from a 2-0 deficit to beat Spartak Moscow 3-2.
Red Star Belgrade, Ajax Amsterdam, and Celtic beat Sūduva Marijampolė, Sturm Graz, and Rosenborg respectively to advance to the third qualifying round of the Champions League.
Celtic manager Brendan Rodgers on Saturday distanced himself from speculation he could succeed Arsene Wenger as Arsenal boss.
Branislav Ivanović had a goal and an assist to help Zenit Saint Petersburg beat Celtic, while RB Leipzig beat Napoli on aggregate despite losing their second-leg match.
Penyokong juara Liga Premier Scotland menyatakan solidariti dengan rakyat Palestin dalam perlawanan menentang kelab Israel, Hapoel Be'er Sheeva untuk kelayakan Liga Juara-Juara.
Fans of Scottish Premier League champions express solidarity with the Palestinian people in match against Israeli opponents in Champions League qualifier.