Naylor played in the Cottagers' reserves defeat to Manchester United last night.
Before the game, Mansfield manager Paul Cox said: "We all wish him the best.
"He just has to forget about who he is up against tonight and enjoy it.
"If he doesn't earn a move it won't be the end of the world. Sometimes these trials are a game of chance and if you don't do well you miss out.
"But he is a lovely lad and deserves success. I know Nigel Clough was very impressed with him last week. But there are now a hell of a lot of other clubs waiting and keeping their eyes on the situation.
"Other clubs have seen him having trails at Premiership and Championship clubs and they are not stupid.
"But until we get a bid that matches our valuation Tom is going nowhere."