Arsene Wenger maintains Arsenal must stay focused on producing "outstanding performances'' for the rest of the campaign rather than worry about what might be going on with their rivals.
The Gunners have so far failed to mount a serious challenge for the Premier League title, and are currently outside the top four as they prepare for Monday night's FA Cup fourth-round replay against Cardiff at Emirates Stadium.
Wenger insists Arsenal must concentrate on turning themselves back into a force.
"I believe [we should] focus on our way to be successful and not too much on the others,'' said the Arsenal manager. "We need outstanding performances until the end of the season and the only way to achieve that is by focusing on our performances.
"If Chelsea gain points Aston Villa will drop, it is all linked together, but if we are consistent we will be there.''
Wenger admitted the decision by Chelsea to remove Scolari, who also had great success in charge of Portugal, from a position he only took up in the summer had come as a "massive surprise''.
"Your reputation helps you to get you a job and to survive a bit longer than usual, but I do not want to interfere with that,'' Wenger reflected. "I am sad when a manager loses his job, but it is very difficult to assess the situation from outside.''
Wenger believes with the appointment of Hiddink, Chelsea will have another top-class coach at the helm.
"He has a strong knowledge of the game and strong personality,'' said Wenger. "He has big experience and he always gets his teams to play the kind of football he wants to play. This is the real art of a good manager.
"Chelsea have gone through a difficult period, but they have been a team that would have come back, even with Scolari. They will certainly come back strongly with Hiddink.''
Arsenal's battling goalless draw at Tottenham last weekend, where they played more than half the game with only 10 men following the dismissal of Emmanuel Eboue, extended an unbeaten run to 11 matches in all competitions.
The FA Cup was the last trophy won by Wenger, back in 2005, and could now present the best chance of silverware this season.
The Arsenal boss, though, maintains it is all about continuing momentum.
"We are unbeaten and want to keep that going in every competition - the longer that lasts, the stronger you will be,'' he said. "If the three draws put together don't look good, then you must put the whole 11 games together and that looks like we are on a run.
"We want to transform that bit of disappointment from a draw into a convincing victory, and the team is on a good way.''