The Celtic boss was made favourite overnight by several bookmakers to take over from David Moyes who will become the new manager at Manchester United on July 1 following the announcement that Sir Alex Ferguson is to retire at the end of the season.
Cardiff manager Malky Mackay, however, also emerged as a strong candidate, with Roberto Martinez of Wigan and Swansea's Michael Laudrup also reportedly in the frame.
Speaking at Lennoxtown ahead of Saturday's Clydesdale Bank Premier League clash with St Johnstone at Parkhead, where the champions will be presented with their SPL trophy, the Northern Irishman was asked if he was flattered by his name being linked with Goodison.
"Of course, it is nice recognition," he said. "Roberto Martinez was favourite yesterday and I'm favourite today, it could be someone else tomorrow.
"But all it is, 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."
Lennon, who revealed skipper Scott Brown will make a surprise return to the squad tomorrow after recovering from surgery to cure an abductor problem, was then asked if Everton was a big enough job to tempt him to leave Celtic.
He said: "It is a bit of a hypothetical question.
"You are all talking about me leaving here and I never said I was leaving.
"Everton are a huge club, a great club with great history and they just lost probably one of the greatest managers in their history.
"It is flattering as I said to be linked with them but that's all it is, just a link."
The former Celtic skipper insists he can improve on what has been a successful season at the Parkhead club but admits timing in football is everything.
"If I am here next season, that's what you look to do, improve every season and I think we have done," he said.
"I think we have progressed this season on and off the field.
"We had the Champions League (last 16), we won the SPL, we are in the Scottish Cup final, the only setback we had was the League Cup semi-final against St Mirren where if we had gone through we would have been challenging for all the domestic trophies which would have been a fabulous season.
"Can you improve on that? Yes, you are always looking to improve and better yourself every year.
"I think all decisions come down to timing. When I got the job here no one gave me a prayer - rookie manager, he has got no chance.
"But opportunities like this come along once in a lifetime and you have to take it.
"So you just never know what's round the corner in football but at the minute I am in a really stable job here with good backing from the board and a good young crop of players."
Lennon expressed his delight that Moyes had got his big move.
"I am delighted for Davie," he said. "For a while I was thinking whether he was going to be overlooked for a big job and undervalued so I am glad he got it.
"He has earned it and I think he will do very well.
"Whoever was going to follow Sir Alex was going to have a hard act to follow but I think the infrastructure at the club is there, the squad is fantastic.
"I am not saying anyone could do it, because it is such a high-pressured job and the spotlight will be on him but he has a great temperament and great knowledge of the game and he is very experienced now."
Lennon was glad to get back to talking about football in Scotland and the visit of St Johnstone."It is going to be very special," he said. "It is a very significant day for the players, the supporters and myself and I want them to enjoy it."
It was expected that Brown would miss the William Hill Scottish Cup final against Hibernian at Hampden later in the month after going under the knife in March.
However, Lennon said: "Brown will be in the squad with a view to playing at some stage tomorrow.
"His rehab has gone really well, we are delighted with that.
"He has been training the last week to 10 days so he just needs football now.
"Obviously with Beram Kayal and Victor Wanyama being suspended (for the cup final), if we can get him up to speed then it is a timely boost for us."
The Hoops boss confirmed that he has been taking a look at 26-year-old French defender Steven Mouyokolo, formerly of Hull and Wolves.
"We have only had him in for two or three days," he said. "I knew about Steven from his time at Hull and Wolves and I liked him then.
"He has had a few injury setbacks in the last year or so but the opportunity came to have a look at him and that's exactly what we are doing at the minute."