The former Newcastle ace had a brief spell at Upton Park, but a relegation release clause in his contract allowed him to leave for a nominal fee when the Hammers failed to avoid the drop three seasons ago.
After joining Newcastle Ba secured a move to Chelsea in January for around £7 million.
The Senegalese forward managed two goals in his 14 Premier League appearances for the Stamford Bridge-based club as he battled with Fernando Torres for a starting spot.
According to the Times West Ham had initially wanted to take Chelsea's Romelu Lukaku on loan for next season, but Jose Mourinho's insistence that the Belgian will be at Stamford Bridge next season has put paid to that.
Instead the Hammers have set their sights on Ba, whose future at Chelsea seems to be somewhat more precarious given recent rumours.
Chelsea have been linked with a move for Napoli forward Edinson Cavani in recent weeks, whose arrival at Stamford Bridge would push Ba down the pecking order.
However Chelsea may be keen to retain his services as a squad player, with Mourinho less than convincing when discussing Fernando Torres's future in west London. The Spaniard has recently been linked with a move to Barcelona.
The Times add that a loan move for new Manchester United signing Wilfried Zaha could also be on the cards.