Benteke, 27, became Palace's record signing when he moved to the south east London club from Liverpool for a fee of £27m during the summer transfer window. The Belgium international has begun to repay that fee with 10 goals this term, with his last two helping the club come from behind against Bolton Wanderers to book their place in the fourth round of the FA Cup.
The former Aston Villa star has however been linked with a move across London. With Diego Costa's long-term future at Stamford Bridge looking bleak with a move to China in the summer now a possibility, Benteke has been shortlisted as a possible replacement for the Spain international in report carried by The Guardian, alongside Everton's Romelu Lukaku and Real Madrid's Alvaro Morata.
The striker has also been linked with a move to Paris Saint-Germain during the January transfer window but he insists he is going nowhere.
When asked about the possibility of leaving, Benteke said: "No, I am very happy here and I want to fight to help the team to move up the table. We deserve it with the players that we have got. Now we have to show it on the pitch.
"It makes me laugh. I am used to [speculation about my future] since I am in England. Now it is maybe two or three years in a row they talk about 'Christian is going to leave.'
"[Allardyce] is a manager with a lot of experience. He has been in the Premier League for a long time and knows how to manage the team out of the position we are in now.
"We are in a dangerous position and we have to look up, because we have the ability and quality in the squad."
Lukaku is also someone being considered as a long-term replacement for Costa should the 28-year-old leave the capital. Like Benteke, however, he has played down talk of a move, telling talkSPORT he is only focused on the Toffees.
"I'm not reading anything about it, I'm just focused with the team and whatever you guys write is whatever you write."