Wolves have lined up a move for the 33-year-old free agent after injuries to forwards Sasa Kalajdzic and Raul Jimenez.
Costa has been without a club since he terminated his contract at Brazilian side Atletico Mineiro in January.
The former Spain international spent three seasons at Chelsea, where he scored 59 goals in 120 games and was a key figure in their 2015 and 2017 title wins.
It is likely that Costa will need time to be ready for action after so long without a club.
But should he join Wolves then one of his first games back in England could be a return to Stamford Bridge when Chelsea host Wolves on October 8.
Wolves can sign Costa outside the transfer window because he is a free agent.