The midfielder suffered a setback soon after his move, with some reports claiming it was a major issue.
Speaking to reporters on Friday, Silva said: "With these type of injuries, you cannot say eight days, 10 days, it is a muscle injury and sometimes you expect three or four weeks and in one moment, the report I have, says it will be two more weeks.
"I think, and what I expect after speaking to the doctor and with Andre on Tuesday, is that maybe after Fulham he will be ready to start full sessions with the team, that is what we expect.
"In this moment, and to be clear with you, and to stop with the rumours, this is new and the doctor said after the Fulham match - one or two days after - he can start full training with the squad."
Two more of Everton's pre-season signings look set to have a bigger role in the coming weeks, as Yerry Mina is nearing a return and Bernard – who impressed off the bench against West Ham – is ready to play 90 minutes.
"Mina is working with the team, for the full week until now," Silva said. "He's getting better every day, getting in good fitness as well."
Silva spoke to Evertontv about Bernard, adding: "Bernard can help with everything we need.
"He did well [against West Ham], he had a good impact in a difficult moment in the match.
"He is a different profile from the other wingers in our squad. He is a quality player and he will help us.
"If I need 90 minutes from him, he is ready. We have one more session and then I will take that decision."