Rumours have emerged in Brazil that Richarlison's agent recently met with Reds manager Jurgen Klopp, prompting talk of a sensational £70 million (£91.2m) transfer to Anfield.
Barcelona, Paris Saint-Germain and AC Milan are also credited with an interest in the forward, who has scored 12 Premier League goals since joining Everton from Watford last year in a deal that could reportedly rise to £50m (£65.1m).
However, when asked on Friday about the Liverpool links, Silva told reporters: "I have to smile.
"This speculation is not important to talk about. Just to smile.
"Richarlison is our player and he is really happy here. I am 100 per cent sure he will keep learning and improving in the next few seasons."
Silva continued: "He's a really important player for us. The club paid a lot of money to sign him. I was 100 per cent sure he can help us and fit really well at our club.
"I asked our club to do everything to sign him. I'm happy, he's happy and my job is to keep working with him.
"He's 21 years old. I don't have doubts he can do more and more and keep improving his performances."
The Brazil striker has already more than doubled his Premier League tally of five goals for the Hornets last season, and could play another six games for the Toffees before the end of the 2018-19 campaign.
His team-mate Jordan Pickford has been criticised after footage emerged of him in a scuffle outside a bar in Sunderland this week, and Silva was displeased by the incident.
"For us as a manager and us as a club I am not happy," he said. "The player is not happy with what happened.
"As football players they have an obligation. It is clear to them. It is a matter for us to remind him. Everything we must do we have already done."
Asked what lessons Pickford, a key member of England's squad in last year's run to the World Cup semi-finals, can take, Silva said: "Many, many things. It's a big learning [curve] to him everything that has happened.
"We have to be aware of these situations. It's done and it happened. It won't happen again. It is my expectation that it won't happen again."