Rhodes was earlier linked with a move to Sunderland, although the report claims the Mackems were eventually put off by the 27-year-old's salary.
The Sheffield Star add that Ipswich then made a tentative enquiry for Rhodes, who began his professional career at Portman Road, after another club showed interest in their ex-Wednesday striker David McGoldrick.
It is claimed, however, that the Tractor Boys left it too late to do a deal for the Owls man.
Rhodes has not started either of Sheffield Wednesday's last two fixtures under Jos Luhukay, and remained on the bench against former club Middlesbrough on Tuesday.
The Scotland international had scored 91 goals in 189 Championship games at the time of his move to Hillsborough a year ago, but has just seven in 43 since then.
Injury-ravaged Wednesday would have been down to just two available strikers - Atdhe Nuhiu and Lucas Joao - had they allowed Rhodes to join Ipswich or Sunderland.
Can Rhodes turn things around at Sheffield Wednesday?