Everton chiefs held crisis talks immediately after defeat at home to Norwich City.
The Telegraph says Silva held talks over his future with Everton majority shareholder Farhad Moshiri and club directors in the wake of the 2-0 defeat.
Sources close to Silva feared he was in danger of losing his job following the loss but it appears he might be given a little more time - with Everton away to high-flying Leicester City next Sunday.
The Everton hierarchy have been desperate to support Silva and are extremely reluctant to make the change.
They met soon after the final whistle with Moshiri holding discussions with chairman Bill Kenwright, chief executive Denise Barrett-Baxendale and director of football Marcel Brands. Silva also later joined them, it is understood.
