However, with former club Atletico Madrid being banned from making transfers until January, it left Costa in a position where he may have had to consider another destination with AC Milan said to be keen on signature, but it appears that they will miss out on the forward.
Costa's time at Chelsea effectively came to an end via a text message sent from Antonio Conte. The Daily Mail believe that an option considered was signing Costa and loaning him out until that time, but they note that Federation Internationale de Football Association prohibit any player being sent out on loan until they are registered.
Costa, who was sold by Atleti for £32m three years ago, has been heavily linked with a return.
The idea of selling Costa elsewhere is remote because of his steadfast determination to consider only a move back to Madrid.
Costa, who has two more years on his contract at Stamford Bridge, is a popular figure in the dressing room but does not want to stay and a festering row between Conte and a senior player will sour the atmosphere.
The 28-year-old has a long track record of excellence in front of goal, but the Blues will reportedly not "pay over the odds" for the ace and prioritise younger additions.
Fans of the Premier League champions will hope there are some incoming players once this Costa deal is agreed.
To circumvent the regulations, the Mirror suggests Costa would be loaned out for six months until 1st January 2018 when his registration could be formalised.
Chelsea might have to swallow financial losses as they subsidise Costa's wages and his value diminishes.
Diario Gol's report claims the Bayern Munich star, who scored 30 goals in the Bundesliga last season, is desperate to win the Champions League.