Mayoral, 23, scored eight goals on loan at Levante this season and has also been trailed by Valencia.
However, Lazio are now close to signing the striker after following up on their initial inquiry.
According to Pedulla, Lazio have agreed to pay €15m plus bonuses, with Real having priority status in any future sale.
There will be no buy-back clause included, but the clubs have good ‘neighbourly’ relations and private agreements.
Mayoral will earn €2.5m-€2.7m plus bonuses per season that could allow him to reach €3m.