Morata has struggled for form and fitness in the second half of the campaign, while Giroud has started only one Premier League match since moving to Stamford Bridge from Arsenal in January.
"I trust them and work with them both to bring the best physical form and condition," Conte told a news conference on Friday.
"Morata is coming from a strange injury in his back, he was a long time out. Giroud is in good form now and working every day. I trust a lot in all my players."
Conte said he could turn to both strikers for Saturday's league clash against Crystal Palace.
"(Against Palace) for sure we have this option to play with Giroud or Morata as number nine. It is an important game and we want to try to get three points," he added.
Chelsea, fifth in the league table, hope to stay close to fourth-placed Tottenham Hotspur, who are five points ahead and occupy the final Champions League qualification spot.
Chelsea have lost four of their last five Premier League games but Palace have not won in six games and have slipped back into the relegation zone.
Defender David Luiz (ankle) and Ross Barkley (hamstring) are unavailable for the Palace visit but midfield N'Golo Kante is back in contention after missing the City defeat as a precaution after fainting at the training ground last week.
"After the situation the doctor brought him to have many check-ups, to understand the physical condition," Conte said.
"But it was all clear. I think that on Sunday he was well but, at the same time, it was right not to take a risk. To give him the opportunity not to play and to rest. But he's okay."
(Reporting by Hardik Vyas in Bengaluru; Editing by Keith Weir)
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