Reports in the Daily Mail claimed that Rodgers was Tottenham's first-choice candidate after Mauricio Pochettino was sacked on Tuesday night however the following morning Spurs appointed Jose Mourinho to take over at the Tottenham Hotspur Stadium.
'I'm very happy at Leicester'
The Northern Irishman has enjoyed a fine start to his tenure as Foxes boss and his seen himself linked with managerial roles at Arsenal and Manchester United but Rodgers reassured fans that he is committed to Leicester.
Speaking to Leicestershire Live he said: "There’s nothing to talk on it. It’s all gossip.
"I’m very happy at Leicester. I’ve only just joined the club. We have a great project here and my focus is on that.
"I’ve learned that you will always be linked with other jobs. What’s important is the now and I’m happy to help the club to develop.
"What happens in football, when you’re doing well, everyone wants to take you away from that. I love my life in Leicestershire.
"I came in with a responsibility to help the club grow. How long that will be, you can never tell, but I’m happy to be here.
'He's a wonderful boy to work with'
The in-form winger is behind Manchester City's Kevin De Bruyne only for assists with four to his name so far and has impressed fans at the King Power Stadium.
The 21-year-old has established himself as one of the first names on the team sheets this season and Rodgers has been delighted with the Englishman's development.
Rodgers said: "He’s got a great profile.
"He’s fast, he’s dynamic, he’s got two good feet. He’s creating goals.
"He’s a wonderful boy to work with. I’ve been delighted with him."
Rodgers was also asked if he could see Barnes forcing his way into Gareth Southgate's plans however Rodgers believes he should focus on club football first.
He said: "If you look at that area of the field, England are very strong with Rashford, Raheem and Sancho.
"It may too soon next summer (for Barnes). He just needs to concentrate on Leicester.