The veteran midfielder's current contract expires this summer.
After the 0-0 draw with Brentford, Silva was asked about Willian's situation.
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He said: "Yes, I was clear in the last two months that we are happy with him and we try to renew the contract with him."
The manager also said of the game: "We showed the motivation and commitment. When you are not motivated you can start to lose focus but we didn't see that in our team. We tried until the last moment to go forward. All the changes I made - and Thomas Frank - was more attacking."