The 26-year-old's loan deal is about to come to an end and his agent Neil Featherby admitted that he is extremely likely to be part of the mass exodus from Elland Road this summer.
"Danny is contracted on loan to Middlesbrough until May 15, and after that he will return to Leeds," Featherby told Sky Sports.
"We appreciate the chances of him staying at Leeds are more than slim, so we will be talking to other clubs. Danny will listen to offers that are made but, at the end of the day, he will do what is right for his family.
"We are more than happy to listen to whatever they (Leeds) bring to the table. But again, we will only do what is right for Danny. We don't want to be obstructive, but we are not going to be rushed into anything."
Leeds have brought in agent Philip Morrison to handle transfers and City are believed to have contacted him to make an enquiry about Mills.