The capital club is determined to recruit the highly talented player who spent last season on loan at Juventus.
Alcaraz, who is highly rated in Italy, is the subject of another loan offer from Lazio.
Per Gazzetta dello Sport, they are said to be offering a loan deal with an obligation to buy.
That would mean Lazio get to keep the player for this season, but have to purchase him before the loan expires and for a set fee.
The fee in question would be anywhere from €10 million to €12 million for Alcaraz.