The 19-year-old caught the eye on Sunday after being given his full Premier League debut in the 1-1 against Liverpool by Blues boss Jose Mourinho.
And experienced Serbian defender Ivanovic admits he was pleased with the way Loftus-Cheek coped when up against Steven Gerrard, Philippe Coutinho and Jordan Henderson.
Ruben Loftus-Cheek made his Premier League debut for Chelsea on Sunday
"He impressed everyone and I hope this is just the beginning of a big career," said Ivanovic, whose side were given a guard of honour by Liverpool before the game following their title success.
"It is the natural thing when the young guys come in to try to help them, but Ruben was very good and he didn’t need help.
"He settled very quickly and he keeps it simple and had a couple of great actions. I hope in the future we have one more great player."
Loftus-Cheek has been a regular for England over the years, picking up caps at U16, U17 and U19 level as well as winning The FA Youth Cup with Chelsea last season.
And he is one of a number of Young Lions who are on the verge of a first-team breakthrough at Stamford Bridge with the likes of Dominic Solanke, Nathaniel Chalobah and Lewis Baker also highly-rated at the west London club.
"We have a great generation of young players and during training with us, they improve and they can be competitive in the team and make our squad bigger," Ivanovic told ChelseaFC.com.
"Not just Ruben, we have a minimum of five or six players who can be in our squad.
"They are still young and they need to fight because this is the period in the next one or two years when they have to prove they are really good."
Loftus-Cheek’s debut came on the back of Chelsea retaining their FA Youth Cup title with a two-legged win over Manchester City last month.
