Super Eagles coach Stephen Keshi said last week the 24-year-old remains in his plans after the national side qualified for this winter's African Nations Cup.
However, Anichebe is focused on building on his - and the Toffees' - good start to the season having been frustrated by two serious knee injuries and a groin problem in the last few years.
"The thing with Nigeria is I am a fan and I follow the games and the team have done really well to qualify," said the forward, who has scored three times in seven matches.
"They have a great bunch of players there but I'm concentrating on here because this is the first time I've stayed fit for a while.
"I am thinking about Everton: they have stuck by me and helped me get back fit so I'm thinking more about cementing [my place in] the side.
"The national team aspect hasn't come into my head. I just want them to do well."
Everton head to bottom side QPR at the weekend and while David Moyes' team are flying high in fourth, having lost just once, Anichebe stressed they cannot take the winless Londoners for granted.
"I think we've done okay: it's been a good start to the season and everyone is on a high and is confident," he told evertontv.
"We need to carry it on though, not get ahead of ourselves and keep playing well.
"They (QPR) are struggling so it is going to be even harder because they need results - they've bought a lot of players and have a lot of expectation on them.
"They haven't really done so well so I am sure they will look to change that against us and we need to be wary of that."