The former Manchester City prospect is unsettled in London and pining for a return home to the Northwest.
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The Sun says while a return to City would be considered, Palmer is keen to hear from United, which is the club he supports.
Indeed, any return to City will only be discussed if manager Pep Guardiola departs. Palmer found himself frozen out by the Catalan before leaving for Chelsea two-and-a-half years ago.
The England international's contract with Chelsea runs to 2033.
