That opening comes in the form of a €42 million release clause in his contract, which allows clubs a chance to begin negotiations with the player.
Arsenal and Chelsea are the clubs most regularly linked with his signature, keen to add a world class striker to transform their title challenge.
There is under a fortnight remaining in the transfer window, and the chance to sign the Brazilian turned Spanish frontman will soon disappear until the summer... right?
Well the summer will provide the chance to head back in for Costa, but it may be a whole lot more expensive.
Italian website Tuttomercatoweb report this evening an exclusive that Atletico Madrid are preparing to increase Costa's release clause.
They report on Manchester United target Koke having his release clause upped to €60 million, when it was originally reported to be a third of that figure.
"In the coming weeks it will happen the same with Diego Costa... Currently, the clause is €42 million, the goal is to increase it. And remove the alarm of the market throughout 2014."
The chances are Costa's clause will not be upped by a little, it will be doubled - into a figure which only the truly crazy football club owner will consider meeting.
The problem for Atletico is right now the clause in Diego Costa's contract is not off-putting as is the intention, but it is inviting.
All of this means any club looking to sign the prolific forward - who has 23 goals in 22 starts this season - will be wise to take note of the reports and make their move to sign him.
If they don't and decide to wait until the summer, it may just be too late...
image: © azuaje