Costa is currently a free agent after terminating his contract with Atletico Mineiro, where he won a domestic double, at the beginning of the year.
The 33-year-old striker has been linked with a number of moves over the past seven months, including a shock switch to Championship club Birmingham City.
But according to Mundo Deportivo via The Sun, the veteran may be returning to his former club in La Liga where he scored ten goals in 16 outings.
According to the report, Vallecano have offered Costa a package worth around £ 70,000 a week for a one-year comeback.
The striker is also thought to be interested in the deal as his family are keen on returning to live in Madrid, the city where Vallecano are based.
Should Vallecano be able to pull off the deal in time then Costa could even make his debut on familiar territory at the weekend.
The Spanish club travel to Old Trafford on Sunday to play Man United in Erik ten Hag’s first home match since taking charge at Old Trafford.
Costa enjoyed a successful three-season stint at Chelsea after joining from Atletico in 2014. He scored 52 goals in 89 Premier League matches for the Blues, winning the title twice and the Carabao Cup during that period.