Gueye was the subject of bids from the Ligue 1 champions before Thursday's deadline, but Everton were able to keep the midfielder.
Marco Verratti's injury has left PSG short in midfield with Leandro Paredes from Zenit their sole major signing during the window.
Gueye signed a new contract running to 2022 last February and a report claimed Silva had threatened to resign if Everton sold the player to PSG.
But speaking at a news conference on Friday, the Toffees boss suggested Senegal international Gueye was never likely to leave.
"It's good for us as a club and for me as a manager," Silva said of Gueye staying at Goodison Park.
"When a club like PSG has a big interest in one of our players it means we're doing a good job. The January market is really tough, because the market is open when you're playing and training.
"The board never told me the deal would be done or not. They never told me to prepare to replace him. Of course it was a good opportunity for Gana, but it's a fantastic opportunity to stay with us also.
"I know Gueye is a good professional and a fantastic boy. He likes our club, he enjoys playing in our club. When PSG comes for one player, he starts thinking about his future.
"Now it's stopped - the market has closed - I've no doubts he will be thinking about playing for Everton again."
After they were thumped 6-2 at home by Tottenham in their last game before Christmas, Everton have recorded three wins and three losses in the Premier League.
The Toffees continue to remain inconsistent and a 12-point deficit to sixth-placed Manchester United indicates the gulf in class between the competition's 'big six' and the rest.
Everton host Wolves on Saturday with Nuno Espirito Santo's side sitting seventh in the table, two points above Everton, who finished eighth last term and are in the same position now.
"Our goal as a team is really clear, to do better than last season in the table," Silva added. "The table for us will be really important in the last match of the season."