"Chelsea has been in discussions with Arsenal for some time over the possible transfer of Ashley Cole," the statement read.
Media reports claim Chelsea were prepared to dole out 16.5 million pounds ($31.3 million) for the versatile defender while Arsenal were asking for 25 million pounds.
"Chelsea has made a very substantial offer for the player. Although discussions have continued, Arsenal's valuation of the player does not match Chelsea's and therefore no agreement can be reached in the current circumstances."
While admitting that Cole is a player of class, Chelsea manager Jose Mourinho voiced his agreement with the club's policy.
"Our offer went to the limit," the Portuguese manager said.
"The club doesn't move ahead one more single pound and I agree completely because our offer is an excellent offer for, of course, an excellent player. But it is in their (Arsenal) hands and they say no."
Mourinho did, however, keep the door ajar for the deal to go through.
"We will look elsewhere, and have been looking elsewhere for some time. Cole is not the only left back in the world.
"But unless we sign another left back, there is a chance it will still happen," he added.