The 25-year-old was first-choice centre-forward for the Blues in the second half of last season under old boss David Moyes, with Nikica Jelavic suffering a dip in form.
However, following Moyes’ exit and Roberto Martinez’s arrival over the summer, no-one is guaranteed a start in the new season and competition for places is high with Anichebe, Jelavic and new signing Arouna Kone all hoping to lead the line.
Anichebe, who hit eight goals last season from 32 appearances, says he doesn’t know if he will get the nod against Norwich in the season opener on Saturday but he will do all he can to persuade Martinez of his talents.
He said: “Some people ask me ‘do you think you will play?’ but I’ve been at Everton since I was young and I want the team to do well.
“We have brought in more competition and it’s great for everyone. Everyone will be fighting for their place.
“I’m at that age where I need to get more consistency. I was happy with how last season went so hopefully this year I can carry on and do well.
“But we’ve got a lot of other great players. Whether I play or not is up to the manager but we’ll all be here fighting together.”
Hibernian head coach Neil Lennon claimed Craig Levein's comments had come back to haunt him after his side's 2-0 victory over Hearts at Easter Road.
Rangers have been handed a boost ahead of the Old Firm derby at Ibrox on Sunday after Alfredo Morelos signed a new deal that keeps him at the club until 2021.