The striker admitted his substitute role has been difficult but he is ready to convince Jose Mourinho to hand him more starts.
Costa has been banned for three matches after being found guilty of violent conduct by the Football Association following a clash with Arsenal defender Laurent Koscielny on Saturday.
The incident, in which Costa appeared to raise his hands to the Gunners defender, was not seen by referee Mike Dean during the match, which Chelsea won 2-0 as Arsenal were reduced to nine men.
Costa was banned for Wednesday's 4-1 Capital One Cup win at Walsall as Remy scored his first goal of the season and the 28-year-old insisted he is ready to perform the striker's physical role ahead of Saturday's trip to former club Newcastle.
"I don't have a choice, I have to do it. When we play for Chelsea it's a question of giving the best 100 per cent, so of course I will do the best I can," he said.
"I think we will miss him because we know how important he is for the team but we are all focused on winning games. Whoever is on the pitch we will try to do the best we can, of course it's a shame for us to lose him.
"Whoever is on the pitch will give their best. It's my old club so it's always a pleasure to play against them. The manager will decide and pick 11 players, we'll see on Saturday."
Remy has made just six Barclays Premier League starts since joining from QPR last summer but has netted seven goals and could deputise for Costa at St James' Park.
He has played for only eight minutes in league action so far this season, and admitted he recent role has been tough.
He said: "It's very difficult, I can't lie. When you come in you have to do the best but when you are not playing much it is more difficult. I cannot complain, I want to play and when the manager wants me to come I just come and try to score goals.
"I just play the way I play and don't put pressure on myself because I know my quality. The manager knows as well that he can use me as a striker or on the side. I don't have any pressure, I just want to feel better and with the game which is coming I maybe have an opportunity to play more. We will see."
Remy scored 14 goals in 27 games for the Magpies on loan from QPR in 2013-14 and backed United, winless and second bottom in the league, to recover from a nightmare start after being dumped out of the League Cup by Sheffield Wednesday.
"I am surprised because they are a big team and strong. I am sure they will get better very soon," he added.