The 63-year-old currently owns the Serie A club Brescia, having sold his participation in Leeds to Andrea Radrizzani three years ago.
Earlier this year, it was reported that Cellino wanted to return to England and was considering clubs in the championship.
Now, Tutto Mercato Web says the blues is one of three sides to be “tested” by Cellino, who hopes to sell in Brescia.
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Trillion Trophy Asia completed its takeover at St Andrew’s in October 2016 after keeping the club afloat when teased within reach of Carson Yeung.
Significant investments have followed in the hopes of reaching the Premier League, but that goal has yet to materialize with repeated problems off the pitch preventing the Blues from continuing.
Cellino was a controversial figure during his three-year stint at Elland Road, going through as many as six managers and cutting costs.
Pep Clotet worked under Cellino in Leeds and said in a recent interview with AS: “I have had English owners, an Italian (in Leeds) and now Chinese.
“Today it’s very important for the coach to understand the owner’s culture in order to work with him.
“In Leeds, with Cellino (Italian), it was a mentality like ours. With the English, working is relatively easy because they play roles very well.
“Instead, the Chinese are very ambitious, they are always thinking about how to improve and it is obviously a very hierarchical culture.
“It may cause a bit of shock at first, but then you enjoy it and you have an obligation to know how to work with them. “
Cellino is also looking into takeover options from Charlton Athletic and Reading.