The Argentine was sacked on Tuesday evening following a severely disappointed start to the season in which the club have only won three out of their opening 12 Premier League games, leaving them languishing in 14th position in the table.
According to The Daily Mail, the Northern-Irishman was targeted by Spurs' chairman Daniel Levy to take over at the Tottenham Hotspur Stadium. The claims suggest that the North-Londoners' submitted an enquiry for Rodgers' signature but were told by the Foxes that it would be 'impossible' for him to depart the King Power Stadium, instead seeing the club turn to former Chelsea and Manchester United boss Jose Mourinho.
Ex-Liverpool manager Rodgers has drawn plenty of admirers since arriving in the East Midlands from Celtic in February. Currently leading the Foxes to second in the Premier League table, Leicester have played some thrilling football and look likely to earn a UEFA Champions League place next season.
He has masterminded some eye-catching results this season, none least their 9-0 victory over Southampton, a 2-0 win over Arsenal and ironically a controversial 2-1 success of Tottenham back in September.
That form has seen Rodgers be linked with a couple of high-profile jobs recently, specifically at Tottenham and also Arsenal as the pressure continues to crank up on Gunners' boss Unai Emery. The 46-year-old's contract at the King Power Stadium is set to run until the summer of 2022.
Top four race
Elsewhere, Tottenham have appointed Mourinho in hope of getting their season back on track. If they are to do that, they need to start cutting the gap to Leicester and the rest of the top four. There are currently 11 points between Spurs and fourth-placed Manchester City, whilst Leicester are one point better off.