Although the two sides agreed to terms on a one-year contract Saturday, the 38-year-old center was not cleared by Rangers team doctors, the source confirmed.
The reason Arnott was not cleared is not immediately known.
The Rangers declined to comment on the deal Saturday night. It is believed that the team was aware of this potential issue and wanted to proceed with caution.
Arnott flew in to New York on Saturday night and was at Madison Square Garden, where he met with multiple team doctors. He has since left the area, a source said.
The deal was slated to be worth a maximum of $1.6 million (pro-rated) with a base salary of $1.2 million.
This likely will not deter the Rangers from looking elsewhere on the free-agent market for depth players to round out their roster.
Coach John Tortorella said before Saturday's 5-2 win against the Toronto Maple Leafs that the team was having discussions about multiple players.