Asencio, 23, is contracted at the Bernabéu until 2031 but faces a difficult fight for minutes after Real Madrid closed the signing of Ibrahima Konaté as well as Marc Cucurella and Denzel Dumfries as full-backs, alongside the renewal of Antonio Rüdiger.
With five centre-backs now on the books and the club seeking yet another left-sided defender, Asencio risks becoming the fifth option in his position.
Madrid are understood to be exploring a structure in which they sell 50 per cent of the player's economic rights, potentially for a fee around his current market value of €20m. No official asking price has been confirmed.
Lazio's interest is genuine but the Gazzetta dello Sport notes the Roman club are aware the deal will be difficult to close — principally because Lazio will not be competing in European football next season, which limits their appeal relative to other potential suitors.
Asencio has been working to convince head coach José Mourinho to retain him in the first-team squad, but with the club's defensive reinforcements almost complete, his departure this summer appears the more likely outcome.
Real Madrid's defensive overhaul this summer has been significant in its scale, and Asencio's situation is a consequence of a club that has invested heavily in improving every position. For a 23-year-old who needs regular football to develop, a move away — even to a club without European football — may represent the most practical path forward.
Whether Jose Mourinho ultimately decides Asencio has a role to play in Madrid's plans remains to be seen. But the direction of travel appears clear, and Lazio's interest, even if complicated by the lack of European football, keeps the possibility of a Serie A move alive.