The Blues have endured a miserable start to the current campaign, and despite a victory over Norwich City this weekend, they remain in the bottom half of the Premier League table.
After 13 matches, the reigning champions have won only four matches, losing seven and managing only 14 points.
Jose Mourinho looks set to delve into the transfer market in January as he looks to give his beleaguered Blues a chance of securing Champions League qualification.
Romano notes that a bid of £9.8 million has been made, and that the EPL giants look set to beat Inter Milan to the 22-year-old frontman.
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However, it is understood that Calleri is seen by Mourinho as one for the future, and will likely be loaned out to another EPL side in order to get experience of life in the top flight.