Having returned to Stamford Bridge after a loan spell at Monaco, Bakayoko has been made available for transfer by the Premier League outfit.
Earlier this week, it was suggested that the Blues were prepared to halve the Frenchman's asking price to £20m in an effort to tempt Milan into an offer.
However, according to Sky Sport Italia, the Italian side are currently showing interest in a loan deal with an option to buy next summer.
The report claims that Milan are willing to pay £2.6m to use Bakayoko during the upcoming season, while holding the choice to push through a £31m permanent transfer in 11 months' time.
Preferring to sell the 25-year-old in the coming weeks, Chelsea are likely to keep their options open at this stage of the transfer window. body check tags ::