The 21-year-old is a graduate of Chelsea’s academy and he has featured 22 times for the club since his debut in 2014.
However, the majority of his appearances have come from the bench and he was likely to be a fringe player at Stamford Bridge this season.
Loftus-Cheek opted to link up with Palace for the 2017-18 campaign and he has turned out on eight occasions despite struggling with injury.
The midfielder was also handed his senior England debut by Gareth Southgate in the goalless draw with Germany on Friday and he put in a man-of-the-match performance.
Redknapp, who managed 17 caps for the Three Lions, believes this campaign could prove to be huge for Loftus-Cheek if he wants to fight for a place at Chelsea next term.
"He (Loftus-Cheek) has to show us now he is the real deal and show everyone at Chelsea, 'Why are you letting me go on loan? I should be in your first team'," Redknapp told Sky Sports.
"He's got all the attributes, the physicality, the touch and the finesse and when he runs with the ball he's got all the power, but I think he can do more.
"I think he can boss games from start to finish, he is so strong, he's 6ft 3in, but he could do it more often.
"He's had a few injuries early in the season, but what he's shown is that if he plays with better players he is a better player. I thought he was exceptional on Friday night and I hope he plays against Brazil."