United boss Jose Mourinho wants the Brazilian midfielder on board in January but faces competition from cross-town rival Pep Guardiola.
And despite their neighbours having superior spending power in the transfer market, Transfer Window podcast guest Ian McGarry says the Red half of Manchester are leading the race to land the Shakhtar man.
"I'd say on paper United are probably favourites to sign Fred," McGarry said on the latest episode.
"However with the spectre of their city rivals hanging over they may find it difficult, particularly with City already having a Brazilian entourage who would make it a lot easier for Fred to fit in there.
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“I'd say on paper United are probably favourites to sign Fred”
Ian McGarry
"And as we know, City's pockets are bottomless so they could easily outbid United if they wanted to.
"I think in this particular window (though) City's need for a central midfielder is less great than United's and would take away from other areas where they need to strengthen, IE: the injury to Gabriel Jesus means they need backup for Sergio Aguero up front and they also need a left-back with Benjamin Mendy still in rehabilitation from his ACL.
"We know from experience that Shakhtar do not sell cheap. They are astute in the transfer market, they buy players when they are younger.
"I believe Fred was bought from Internacional for around £15m and they are looking at upwards of £35m-£40m minimum.
"As we've reported before, Jose has around £90m to spend in this window so that would represent half, in terms of fee of that."