While Max Verstappen struggles, Australian Ricciardo is in top form but out of contract at the end of 2018.
"He's made himself a few million more expensive," 2016 world champion Nico Rosberg commented after Ricciardo won at Monaco.
Lewis Hamilton agreed, saying: "I hear he earns less [than Verstappen], even though he does more. He's currently the leader at Red Bull."
Red Bull boss Christian Horner said that the team wants Ricciardo to stay.
"Daniel knows the capabilities of the team, he sees how well the team suits him, and I hope that in the next few months we will settle all the issues," he said.
However, Ricciardo remains linked with a potential switch to Mercedes or Ferrari.
Red Bull's Dr Helmut Marko told Auto Bild after Monaco: "For us, nothing changes.
"We want to keep him and Daniel knows it. Why should he go to Mercedes or Ferrari? To be a number 2 driver?
"With us, Daniel has equal opportunities with the same equipment and no team orders. I think he knows that too," he added.
Marko said that he wants to get a new contract signed "as soon as possible".