23-year-old Mayoral has been close to joining Lazio, with reports of the Biancocelesti having a €15m bid accepted.
But they have placed the deal on standby, giving clubs such as Valencia and Fiorentina a chance to get involved.
And Gianluca Di Marzio reports that Valencia have now made an official bid of €15m plus bonuses to Madrid.
Valencia are in a hurry to close the deal and Lazio must react quickly if they still want Mayoral.
Lazio are close to signing Vedat Muriqi from Fenerbahce for €18m, which could impact their pursuit of Mayoral.