The Blues striker has been hampered by hamstring problems since before making the switch from La Liga champions Atletico Madrid during the off-season.
Costa was forced off in the early stages of Atleti’s last two games of the season against Barcelona and Real Madrid, the latter in the UEFA Champions League final.
However, the 25-year-old has featured in all six Premier League matches for the west Londoners this season, finding the back of the net eight times already, including a hat-trick against Swansea.
Mourinho feels the October international break would provide his recent signing with the perfect opportunity to rest up and give the injury time to recover.
But after completing the full 90 minutes in Tuesday’s 1-0 win over Sporting CP in the Champions League, Costa believes he is fit enough to be considered for Vicente del Bosque’s squad for the clashes against Slovakia and Luxembourg.
Asked if the situation would spark a club versus country war, he told Marca: “I do not believe that could happen. I have already had enough with the issue about Brazil.
“Now I must stay relaxed to be able to work and do things well, with the national team too. I hope I am okay to go with Spain.
“If I played 90 minutes it is clear that I am fine, I am feeling better all the time, and it is the boss’ decision [del Bosque].”