Asensio had been tipped to leave Real as, despite his reputation as one of the best young players in the world, he started just 19 times in La Liga last season. But Gaggioli anticipates a greater role for his 22-year-old client with Los Blancos in the upcoming campaign.
"Marco won't move, he'll stay with Real Madrid. He's improving all the time. Next season I think he'll be very important in Madrid," Gaggioli told CalcioMercato.
The Liverpool gossip began earlier this summer when there was a clamour based on 'reports in Spain' that the Reds were prepared to spend around £150m on Asensio as part of plans to replace Philippe Coutinho after the Nabil Fekir deal fell through.
Asensio remains under contract with Real until the summer of 2023 after signing a new deal with the reigning European champions just last September. That extension also crucially served to raise a relatively low €80m buyout clause to a prohibitive €700m.
Asensio was part of Spain's World Cup squad this summer, featuring as a late substitute in group games against Iran and Morocco, before playing 104 minutes of the last 16 clash with Russia that went all the way to a penalty shootout.
With his World Cup over surprisingly early, it means Asensio and the rest of Real's Spanish players could play a more active role in pre-season than first thought.
The first friendly against Manchester United on 31st July may come too soon, but further tour games against Juventus, which could yield an early reunion with Cristiano Ronaldo, and Roma on 4th and 7th August respectively might see Asensio return to club action.