Neil Lennon is reportedly keen to bolster his attacking options despite bringing in Patryk Klimala from Polish side Jagiellonia Bialystok and seeing Leigh Griffiths return to action.
Sources close to the Hoops told Football Insider that the Northern Irishman is still seeking reinforcements up top and is said to be keen on Rhodes.
Wednesday are pursuing Crystal Palace striker Connor Wickham and could let the 14-cap Scotland international leave Hillsborough if they can do a deal for the Eagles man.
Celtic's need to beef up their forward options intensified in midweek when Mikey Johnston suffered suspected knee ligament damage in his side's 3-0 win over St Johnstone on Wednesday night.
Rhodes has flitted in and out of the Owls' squad this season, making just 15 appearances in all competitions. He scored nine goals durinf a loan spell at Norwich last season, helping the Canaries to promotion.