"We are aware of the situation and we are working with the club to investigate," a Thames Valley Police spokesman told BBC Sport on Thursday.
Both players were involved in incidents in Reading’s Premiership game against Chelsea last month that resulted in Cech and Cudicini ending up in hospital with head injuries.
Czech international Cech is expected to sit out the season with a fractured skull after a first-minute collision with Hunt.
"The club is dealing with all my letters and I don't want to say any more," said Hunt.
His replacement, Cudicini, was knocked out in an aerial challenge with Sonko in the final minute and had to be stretched off.
Chelsea skipper John Terry had to take goalkeeper duties in the match that ended in a 1-0 win for the Blues.
According to the Reading Chronicle newspaper, one letter said: "We are going to kill you for what you did to our 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," Reading manager Steve Coppell 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."
On the other hand, Chelsea condemned the letters in a statement.
"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."
"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," the statement added.