Despite ongoing speculation regarding a number of potential incomings, Chelsea are yet to make a first-team addition this summer.
However, it appears that progress is being made with Kalidou Koulibaly, Nathan Ake and Raheem Sterling all being tipped to sign for the Blues in the coming days.
Head coach Thomas Tuchel continues to deliberate over which other attackers to target with Leeds United winger Raphinha having seemingly decided to move to Barcelona.
According to the Evening Standard, Leao remains on Chelsea's radar and an enquiry has been made with regards to his availability.
The 23-year-old contributed 11 goals and eight assists as Milan ended their lengthy wait to win another Serie A title last season.
The Portugal international currently has two years remaining on his contract, leaving the versatile attacker at somewhat of a crossroads.
Milan are currently attempting to tie the player down to a new long-term deal, one which would include a release clause well in excess of £100m.
However, Leao is naturally attracting widespread interest from elsewhere, leaving both player and club with decisions to make before the end of August.
Milan are said to be in the process of trying to sign Chelsea playmaker Hakim Ziyech, although it is not believed that the two situations could be linked in the future.
Earlier in the month, it was reported that each of Newcastle United and Paris Saint-Germain were both monitoring any developments involving Leao.
Both clubs are in a position to match any demands set out by Milan, but the Magpies cannot offer Champions League football and Leao may not be regarded as first choice at PSG.
Leao has made a total of 76 starts and 39 substitute appearances for Milan since signing from Lille in a €23m deal three years ago.