Lennon has been backed into as low as 16/1 with Sky Bet to replace Paolo Di Canio, who was sacked on Sunday after a miserable start to the Premier League campaign.
But speaking ahead of the Hoops' Scottish League Cup home tie against Morton on Tuesday night, he distanced himself from the claims.
"I don't like answering questions on this kind of thing," he told Sky Sports News.
"I'm not aware of me being linked with anything. You are asking the wrong person.
"Maybe you should ask the people linking me with the jobs. I'm not aware of who they are. I'm very, very happy doing what I'm doing at the minute."
Of the match with Morton, in the only domestic competition he has yet to win, Lennon revealed he would rest some of the players in action in the 2-1 victory over St Johnstone at the weekend.
"The League Cup was the first competition I won as a player here and first I won as a captain," he added, "so it does have some significance for me personally.
"We have only won the trophy 14 times. Even if you go back to Mr Stein's time, it's not been a competition we have dominated. But it's a competition we are in and one we want to win.
"There are a few players who will need a break and we will change the team from the weekend. But they won't be drastic changes and we will treat Morton with the respect they deserve."