City’s offer for Declan Rice is believed to involve an £80m initial payment but still falls short of the £100m West Ham are looking for.
Arsenal have, so far, been unable to hit that figure either.
Their latest bid, an initial £75m in four payments, plus £15m in add-ons, was rejected by the Hammers last week.
Sources believe discussions around Rice are now reaching their final stages and some kind of agreement is likely.
Although they have lined up Chelsea’s Mateo Kovacic in a £25m deal, the loss of Ilkay Gundogan to Barcelona means City manager Pep Guardiola is keen to bolster his midfield options.
Rice, who became the first West Ham captain since Bobby Moore to lead the club to European success with the victory over Fiorentina in the Europa Conference League final, is viewed as the ideal candidate.