Manager David Moyes said Anichebe has earned his place on merit - and his fifth goal in eight league starts in the 3-3 draw against Aston Villa on Saturday appeared to back that up - as Jelavic has lost his way in front of goal with his last top-flight goal almost two months ago.
But Anichebe said: "I wouldn't look too far into him not playing. Nikica has been unbelievable since he came to us and his record speaks for itself (18 goals in 45 appearances)."
He added: "I was injured for two months and he took the burden on his own and he has been playing on his own every game. There comes a time when you have to take him out because he is pretty tired but the best of him will come. He has been playing for a long time on his own. Now I am back it is probably good time to give him a rest.
"I talk to him all the time and some of the positions I am getting into is because of him, he has helped me get into more goalscoring positions.
"We can play together. If he doesn't play, if I don't play, it is not a big deal."
Moyes believes Anichebe's form is down to improved self-belief.
"I think there have been a lot of times when Victor has been questioned and maybe even our faith in him at times," he said. "But I hope he has seen we always believed there was a really good player in there if we could get it out of him.
"He has been needing support from the crowd because for a long time I think he was probably believing they weren't behind him or didn't value him as a player and maybe some of the things he has done on the pitch you wouldn't have (done so).
"But we have tried to keep with him and work with him and he made a big contribution, scoring a goal, was a threat and was challenging high up the pitch. He is doing really well for us at the moment. We have brought him in and given Jela a breather and I think Victor is deservedly playing up front at the moment by how he is doing."