Brazilian-born Costa chose to represent Spain ahead of native land in a move which caused controversy in South America in September.
The Atletico Madrid forward has netted 13 goals so far this season, putting him on level terms with Cristiano Ronaldo at the head of the La Liga goal-scorers.
However Negredo, who himself has four Premier League goals this term, is undeterred by the inclusion of Costa and insist he has no fear he will be in Rio next summer.
"I have to do my job, he will do his, and it is up to the coach," Negredo told El Desmarque Radio.
"I have all the respect in the world for Diego Costa, but I am not scared of anything."
"The one with the problem is the manager, Vicente del Bosque.
"I do not feel like the undisputed starter. The number nine spot in the Spain team is a difficult one, given all of the debate there is, the excellent form the strikers are displaying and the great number of them to choose from."
The addition of Costa provides options for Del Bosque and the manager plans to explore all avenues in the months leading up to the World Cup.
"He is playing very well, and finds himself in peak form," the coach explained.
"Now, he is another option. Diego Costa does not take away, he is a plus. It is obvious we have made efforts to bring him to us.
"Credit is not limitless for anyone, but from here until March we have time to see how things pan out. He is under the same conditions as the rest."