Chelsea travel to Atletico Madrid on Wednesday for their second Champions League group stage tie.
It will be Morata's first return to Spain since leaving Atletico's rivals Real Madrid in the summer.
The Spaniard has started his Stamford Bridge career in fine form, scoring six goals in as many league games, including a hat-trick last weekend.
Goalkeeper Courtois used to play for Diego Simeone's side but is expecting to receive a warmer reception than Morata on his return.
“Alvaro played a lot of games against Atlético," said the shot-stopper.
"I think it will be a big game against his old rivals.
"It will be more friendly for me but between the 90 minutes I will also be a rival of Atletico.”
The midweek clash will be Atletico's first European fixture in their new stadium, the Wanda Metropolitano.
And Courtois is looking forward to playing in the new venue.
“I remember being at the presentation of the new stadium when they first revealed it,” he said.
“I went there to see the place when there was only one stand, the old one, and they were doing the groundwork.
"It will be nice to see it."
Chelsea will go into the clash full of confidence after hammering Stoke City 4-0 on Saturday.
The Champions League fixture is followed by the visit of Manchester City this weekend.
Pep Guardiola's side have been in scintillating form this season.
But Courtois believes Chelsea will continue their strong start to the campaign.
“We have started this difficult week well with a good victory against Stoke and hopefully Wednesday and Saturday we will carry this good form on," said the Belgian.
“The top teams are doing well this season and we are happy to be close to the top.
"If we want to close that gap we need to try and win next week.”
Chelsea beat Qarabag 6-0 in their European opener, while Atletico drew 0-0 at Roma.
