"We are aware of the situation and we are working with the club to investigate," a Thames Valley Police spokesman said on Thursday.
Hunt and Sonko were involved in controversial incidents in a Premier League match against Chelsea last month that resulted in both Chelsea's goalkeepers ending up in hospital with head injuries.
Hunt was cleared of foul play by the Football Association after a first-minute collision with Petr Cech. The Czech international sustained a fractured skull and is not expected to play again this season.
In the final minute of the game Cech's replacement Carlo Cudicini was knocked out in an aerial challenge with Sonko and needed oxygen before being taken off on a stretcher.
Cudicini's injuries were not serious and he has since returned to action for the English champions.
Reading manager Steve Coppell tried to play down the threats to his players.
"We passed the mail to the police, but no extra security precautions were taken, the players weren't affected and it's not an issue," he told the club's website.
"We wanted to keep it quiet, and didn't make an issue of it. We went through the proper channels and hoped it would die a death."
Reading skipper Graeme Murty added: "The last thing we want is to stir up another hornet's nest. We just want to play football."
Chelsea said they would assist any police investigation, although emphasised that there was no link to fans of the club.
"At this stage there is absolutely nothing to suggest that these threats came from genuine Chelsea fans and the club has not been contacted by the police," a club statement said.
"Naturally we condemn any threats of this nature and we will assist the police fully if, and we stress if, there is any evidence linking this to any of our supporters."
