Sterling is close to a new deal from the reigning Premier League champions which will see him earn £300,000-a-week in wages.
While City think highly of the attacker, Sterling has frequently come under criticism from media and fans.
However, the 23-year-old Sterling enjoyed an excellent season in 2017-18 as part of City’s record-breaking Premier League title-winning side, scoring 18 goals and adding 11 assists in the league.
He has shown no signs of slowing down this season, scoring six goals and adding five assists in nine top flight games thus far.
And those numbers are precisely why Carragher thinks Sterling is worthy of his new deal, despite criticism the former defender feels is overblown.
"We are hearing reports that Sterling is on the verge of signing a big contract and maybe there are eyebrows raised because of the figures involved, but when you look at the stats, he is in the company of players who are earning those figures and people are saying are the best players in the league,” Carragher said on Sky Sports.
"Go back to England in the summer and this lad gets far too much criticism. When you look at what this lad is achieving, the move to Manchester City, the pressure and the price-tag. Plus Pep Guardiola, who everyone wants to play for, came in and can get players from Spain and anywhere in the world.
"This young English lad is thriving under maybe the best manager in the world and in the best team in the league. He deserves everything he gets."
The one thing Carragher does think Sterling needs to work on is his England output.
The attacker finally broke a three-year goal drought for the Three Lions in a 3-2 win against Spain, and Carragher hopes Sterling can translate some of his club form over to international play.
Carragher added: "On the back of the Spain game against England, hopefully we will see a bit more of that because he does need to up his stats in terms of goals and assists for the national team.
"What he is doing for Manchester City now… we always talk about Sergio Aguero, David Silva and Kevin De Bruyne, but he is now in that company."