Italian newspaper La Gazzetta dello Sport reports that Walter Mazzari has sent his main scout to monitor the Nigerian whose contract at Stamford Bridge lasts till 2017.
Mikel has seen his Chelsea place come under threat with the arrival of Nemanja Matic in January and has also been curtailed by minor injuries.
Rated at 15 million Euros, the prize could be too high for the San Siro club who are also mauling a loan move in the summer transfer window.
Inter will also wait to see if Chelsea coach Jose Mourinho has an interest in signing any Inter player which could result in Mikel being thrown into the negotiations.
Mikel is expected to lead Nigeria’s charge at the World Cup in June and an impressive performance with the Super Eagles would shoot up his profile and asking fees.