Moyes is leaving Goodison Park to take over at Manchester United on 1 July to replace the retiring Sir Alex Ferguson.
A rush of money on 41-year-old Lennon, who has guided Celtic to two successive Scottish Premier League titles in the last two years and steered them to the last 16 of the Champions League this season, saw his odds cut from 12/1 to odds-on favourite for the Toffees job.
However, while admitting he is flattered to be connected with the Merseyside club, Lennon says he is already planning for next season with the Bhoys.
"Everton are a huge club with a huge history," said Lennon. "It's flattering to be linked but that's all it is, a link.
"All of it is speculation. I have a job here, I have a great job, a great set of players, a great support, so I am pretty happy here.
"I have a rolling contract. We're already looking at Champions League preparation and bringing in new players.
"It's not up to me if I'm ready for England, it's for other people to decide."
Wigan boss Roberto Martinez has also been linked with the Everton job but says he will not listen to any approaches until the season ends with the Latics targeting FA Cup glory and battling to avoid relegation from the Premier League.
And another potential candidate, Michael Laudrup, is not interested in leaving Swansea.
The Dane's agent Bayram Tutumlu said: "He will not be changing clubs. He likes Swansea and is very settled."