City manager Pep Guardiola is a fan of the Brazil international and is keen to bring him in during the January market.
The Daily Mail says Guimarães has a buyout clause in his contract set at £100m.
However, City hope to lower the price by including Matheus Nunes, 26, in their bid.
Guimaraes admitted earlier this season: "That Manchester City shows interest shows that I am at a high level, but it was nothing more than interest.
"I know that Guardiola likes my football, it is normal to have good coaches who admire your football. We have spoken once, I praised his work, he praised my work, but it was nothing more than that."
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