De Leeuw joined County on a two-year deal from Cambuur Leeuwarden last summer and played a key role in helping the club to preserve their Scottish Premiership status.
The Dutchman is reportedly attracting interest from clubs in several countries, although County have received no offers as yet for the 26-year-old.
County sold de Leeuw’s compatriot Kevin Luckassen to Slovan Liberec in January and Adams is aware that every player has his price.
“We don’t want to see Melvin go but we also know that, when you score 10 goals in the top division, there’s going to be interest,” said Adams in the Daily Record.
“We saw that interest in Kevin and we haven’t been surprised to see it in Melvin as he’s done well for us.
“We haven’t had any formal approaches but we are aware of people watching him.”