FcInterNews reports City made a cheeky loan bid for Murillo during the winter market. The English giants wanted to sign the 25 year-old to the end of the season.
However, Inter management gave the offer short shrift, insisting the Colombia international was unavailable.
Indeed, Inter now want to discuss new terms with the centre-half.
Murillo is currently on €1.3 million-a-year, with Inter prepared to upgrade that to €2 million-a-year.