Silva has been a key part of three title-winning teams at the Etihad Stadium and been capped 64 times by Portugal, but Gundogan believes he is not fully appreciated.
"I think he's very underrated," Gundogan said. "He puts so much effort into everything he does, on the pitch to make it easier for us, not just for himself.
"There might be a danger that sometimes he is not appreciated enough, but we know in the club how important he is for us, how appreciated he is in the team and we are very happy that he's here and having such an incredible season."
Silva was open to leaving City in the summer, but with no suitable offers arriving he stayed at the club to begin his fifth season in England.
He was on the bench for the opening day defeat to Tottenham but has since started every game in the league and Champions League, scoring four goals including one in the derby victory over Manchester United at Old Trafford.
Sources have told ESPN that a lack of game time has also led Raheem Sterling to consider his options, but Gundogan is hopeful the pair are back to their best.
"The only thing you can do is try to support them as much as possible, to help them to train well," he said. "In our team the players know their responsibility, they know we are all professionals even though we face difficult periods in our career, we need to be able to deal with that... all of us had to do it in our careers.
"It's something you have to get used to and deal with -- it's disappointment and frustration.
"But they both feel very comfortable in the team with the players we have here. There's a lot of good friendships and I don't think it was ever an issue. The other players don't feel they have to do much, we knew they had enough quality to come back."
With City missing Kevin De Bruyne, Jack Grealish, Phil Foden and Ferran Torres, Silva and Sterling have started the last three games. All three have been victories -- including the impressive 2-1 win over Paris Saint-Germain -- and Gundogan believes the injured players may face a battle to get back into the team.
"Everyone knows they have to be at their best to get into the first XI and also when everyone is fit, you have to accept that you might have to sit on the bench as other players are there who have the quality to play," he added.
"If they train well every single day on the training pitch, that's also crucial. So we just don't need 11 great players on the pitch.
"We also need the great ones who sometimes need to be outside. It's not always easy to accept that role but it's crucial to win the biggest games and titles."